diff --git a/doc/api/next_api_changes/deprecations/20620-ES.rst b/doc/api/next_api_changes/deprecations/20620-ES.rst
new file mode 100644
index 000000000000..02ac7e574603
--- /dev/null
+++ b/doc/api/next_api_changes/deprecations/20620-ES.rst
@@ -0,0 +1,18 @@
+``NavigationToolbar2.set_cursor`` and ``backend_tools.SetCursorBase.set_cursor``
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+Instead, use the `.FigureCanvasBase.set_cursor` method on the canvas (available
+as the ``canvas`` attribute on the toolbar or the Figure.)
+
+``backend_tools.SetCursorBase`` and subclasses
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+``backend_tools.SetCursorBase`` was subclassed to provide backend-specific
+implementations of ``set_cursor``. As that is now deprecated, the subclassing
+is no longer necessary. Consequently, the following subclasses are also
+deprecated:
+
+- ``matplotlib.backends.backend_gtk3.SetCursorGTK3``
+- ``matplotlib.backends.backend_qt5.SetCursorQt``
+- ``matplotlib.backends._backend_tk.SetCursorTk``
+- ``matplotlib.backends.backend_wx.SetCursorWx``
+
+Instead, use the `.backend_tools.ToolSetCursor` class.
diff --git a/lib/matplotlib/backend_bases.py b/lib/matplotlib/backend_bases.py
index 8a5ba25a704f..5be359b9c426 100644
--- a/lib/matplotlib/backend_bases.py
+++ b/lib/matplotlib/backend_bases.py
@@ -2011,6 +2011,24 @@ def release_mouse(self, ax):
         if self.mouse_grabber is ax:
             self.mouse_grabber = None
 
+    def set_cursor(self, cursor):
+        """
+        Set the current cursor.
+
+        This may have no effect if the backend does not display anything.
+
+        If required by the backend, this method should trigger an update in
+        the backend event loop after the cursor is set, as this method may be
+        called e.g. before a long-running task during which the GUI is not
+        updated.
+
+        Parameters
+        ----------
+        cursor : `.Cursors`
+            The cursor to dispay over the canvas. Note: some backends may
+            change the cursor for the entire window.
+        """
+
     def draw(self, *args, **kwargs):
         """
         Render the `.Figure`.
@@ -2864,9 +2882,6 @@ class NavigationToolbar2:
       :meth:`save_figure`
          save the current figure
 
-      :meth:`set_cursor`
-         if you want the pointer icon to change
-
       :meth:`draw_rubberband` (optional)
          draw the zoom to rect "rubberband" rectangle
 
@@ -2914,7 +2929,7 @@ def __init__(self, canvas):
         canvas.toolbar = self
         self._nav_stack = cbook.Stack()
         # This cursor will be set after the initial draw.
-        self._lastCursor = cursors.POINTER
+        self._lastCursor = tools.Cursors.POINTER
 
         self._id_press = self.canvas.mpl_connect(
             'button_press_event', self._zoom_pan_handler)
@@ -2983,16 +2998,16 @@ def _update_cursor(self, event):
         """
         if self.mode and event.inaxes and event.inaxes.get_navigate():
             if (self.mode == _Mode.ZOOM
-                    and self._lastCursor != cursors.SELECT_REGION):
-                self.set_cursor(cursors.SELECT_REGION)
-                self._lastCursor = cursors.SELECT_REGION
+                    and self._lastCursor != tools.Cursors.SELECT_REGION):
+                self.canvas.set_cursor(tools.Cursors.SELECT_REGION)
+                self._lastCursor = tools.Cursors.SELECT_REGION
             elif (self.mode == _Mode.PAN
-                  and self._lastCursor != cursors.MOVE):
-                self.set_cursor(cursors.MOVE)
-                self._lastCursor = cursors.MOVE
-        elif self._lastCursor != cursors.POINTER:
-            self.set_cursor(cursors.POINTER)
-            self._lastCursor = cursors.POINTER
+                  and self._lastCursor != tools.Cursors.MOVE):
+                self.canvas.set_cursor(tools.Cursors.MOVE)
+                self._lastCursor = tools.Cursors.MOVE
+        elif self._lastCursor != tools.Cursors.POINTER:
+            self.canvas.set_cursor(tools.Cursors.POINTER)
+            self._lastCursor = tools.Cursors.POINTER
 
     @contextmanager
     def _wait_cursor_for_draw_cm(self):
@@ -3009,10 +3024,10 @@ def _wait_cursor_for_draw_cm(self):
             time.time(), getattr(self, "_draw_time", -np.inf))
         if self._draw_time - last_draw_time > 1:
             try:
-                self.set_cursor(cursors.WAIT)
+                self.canvas.set_cursor(tools.Cursors.WAIT)
                 yield
             finally:
-                self.set_cursor(self._lastCursor)
+                self.canvas.set_cursor(self._lastCursor)
         else:
             yield
 
@@ -3230,6 +3245,7 @@ def save_figure(self, *args):
         """Save the current figure."""
         raise NotImplementedError
 
+    @_api.deprecated("3.5", alternative="canvas.set_cursor")
     def set_cursor(self, cursor):
         """
         Set the current cursor to one of the :class:`Cursors` enums values.
@@ -3239,6 +3255,7 @@ def set_cursor(self, cursor):
         called e.g. before a long-running task during which the GUI is not
         updated.
         """
+        self.canvas.set_cursor(cursor)
 
     def update(self):
         """Reset the axes stack."""
diff --git a/lib/matplotlib/backend_managers.py b/lib/matplotlib/backend_managers.py
index a8d493aea177..6d2d9595545d 100644
--- a/lib/matplotlib/backend_managers.py
+++ b/lib/matplotlib/backend_managers.py
@@ -254,6 +254,16 @@ def add_tool(self, name, tool, *args, **kwargs):
                                'exists, not added')
             return self._tools[name]
 
+        if name == 'cursor' and tool_cls != tools.SetCursorBase:
+            _api.warn_deprecated("3.5",
+                                 message="Overriding ToolSetCursor with "
+                                 f"{tool_cls.__qualname__} was only "
+                                 "necessary to provide the .set_cursor() "
+                                 "method, which is deprecated since "
+                                 "%(since)s and will be removed "
+                                 "%(removal)s. Please report this to the "
+                                 f"{tool_cls.__module__} author.")
+
         tool_obj = tool_cls(self, name, *args, **kwargs)
         self._tools[name] = tool_obj
 
diff --git a/lib/matplotlib/backend_tools.py b/lib/matplotlib/backend_tools.py
index 15654cce2073..cc81b1f9269b 100644
--- a/lib/matplotlib/backend_tools.py
+++ b/lib/matplotlib/backend_tools.py
@@ -22,7 +22,7 @@
 
 import matplotlib as mpl
 from matplotlib._pylab_helpers import Gcf
-from matplotlib import cbook
+from matplotlib import _api, cbook
 
 
 class Cursors(enum.IntEnum):  # Must subclass int for the macOS backend.
@@ -266,24 +266,28 @@ def _add_tool_cbk(self, event):
         self._add_tool(event.tool)
 
     def _set_cursor_cbk(self, event):
-        if not event:
+        if not event or not self.canvas:
             return
         if (self._current_tool and getattr(event, "inaxes", None)
                 and event.inaxes.get_navigate()):
             if self._last_cursor != self._current_tool.cursor:
-                self.set_cursor(self._current_tool.cursor)
+                self.canvas.set_cursor(self._current_tool.cursor)
                 self._last_cursor = self._current_tool.cursor
         elif self._last_cursor != self._default_cursor:
-            self.set_cursor(self._default_cursor)
+            self.canvas.set_cursor(self._default_cursor)
             self._last_cursor = self._default_cursor
 
+    @_api.deprecated("3.5", alternative="figure.canvas.set_cursor")
     def set_cursor(self, cursor):
         """
         Set the cursor.
-
-        This method has to be implemented per backend.
         """
-        raise NotImplementedError
+        self.canvas.set_cursor(cursor)
+
+
+# This exists solely for deprecation warnings; remove with
+# SetCursorBase.set_cursor.
+ToolSetCursor = SetCursorBase
 
 
 class ToolCursorPosition(ToolBase):
diff --git a/lib/matplotlib/backends/_backend_tk.py b/lib/matplotlib/backends/_backend_tk.py
index a7d123594656..27cfc69e2bd9 100644
--- a/lib/matplotlib/backends/_backend_tk.py
+++ b/lib/matplotlib/backends/_backend_tk.py
@@ -794,6 +794,7 @@ def remove_rubberband(self):
             del self.lastrect
 
 
+@_api.deprecated("3.5", alternative="ToolSetCursor")
 class SetCursorTk(backend_tools.SetCursorBase):
     def set_cursor(self, cursor):
         NavigationToolbar2Tk.set_cursor(
@@ -907,7 +908,6 @@ def trigger(self, *args):
 
 backend_tools.ToolSaveFigure = SaveFigureTk
 backend_tools.ToolConfigureSubplots = ConfigureSubplotsTk
-backend_tools.ToolSetCursor = SetCursorTk
 backend_tools.ToolRubberband = RubberbandTk
 backend_tools.ToolHelp = HelpTk
 backend_tools.ToolCopyToClipboard = backend_tools.ToolCopyToClipboardBase
diff --git a/lib/matplotlib/backends/backend_gtk3.py b/lib/matplotlib/backends/backend_gtk3.py
index 5747e6ced397..fc24f3d614bc 100644
--- a/lib/matplotlib/backends/backend_gtk3.py
+++ b/lib/matplotlib/backends/backend_gtk3.py
@@ -90,7 +90,7 @@ def _create_application():
 
 @functools.lru_cache()
 def _mpl_to_gtk_cursor(mpl_cursor):
-    name = {
+    name = _api.check_getitem({
         Cursors.MOVE: "move",
         Cursors.HAND: "pointer",
         Cursors.POINTER: "default",
@@ -98,7 +98,7 @@ def _mpl_to_gtk_cursor(mpl_cursor):
         Cursors.WAIT: "wait",
         Cursors.RESIZE_HORIZONTAL: "ew-resize",
         Cursors.RESIZE_VERTICAL: "ns-resize",
-    }[mpl_cursor]
+    }, cursor=mpl_cursor)
     return Gdk.Cursor.new_from_name(Gdk.Display.get_default(), name)
 
 
@@ -188,6 +188,14 @@ def __init__(self, figure=None):
     def destroy(self):
         self.close_event()
 
+    def set_cursor(self, cursor):
+        # docstring inherited
+        window = self.get_property("window")
+        if window is not None:
+            window.set_cursor(_mpl_to_gtk_cursor(cursor))
+            context = GLib.MainContext.default()
+            context.iteration(True)
+
     def scroll_event(self, widget, event):
         x = event.x
         # flipy so y=0 is bottom of canvas
@@ -533,13 +541,6 @@ def set_message(self, s):
         escaped = GLib.markup_escape_text(s)
         self.message.set_markup(f'<small>{escaped}</small>')
 
-    def set_cursor(self, cursor):
-        window = self.canvas.get_property("window")
-        if window is not None:
-            window.set_cursor(_mpl_to_gtk_cursor(cursor))
-            context = GLib.MainContext.default()
-            context.iteration(True)
-
     def draw_rubberband(self, event, x0, y0, x1, y1):
         height = self.canvas.figure.bbox.height
         y1 = height - y1
@@ -717,6 +718,7 @@ class PseudoToolbar:
         return NavigationToolbar2GTK3.save_figure(PseudoToolbar())
 
 
+@_api.deprecated("3.5", alternative="ToolSetCursor")
 class SetCursorGTK3(backend_tools.SetCursorBase):
     def set_cursor(self, cursor):
         NavigationToolbar2GTK3.set_cursor(
@@ -850,7 +852,6 @@ def error_msg_gtk(msg, parent=None):
 
 backend_tools.ToolSaveFigure = SaveFigureGTK3
 backend_tools.ToolConfigureSubplots = ConfigureSubplotsGTK3
-backend_tools.ToolSetCursor = SetCursorGTK3
 backend_tools.ToolRubberband = RubberbandGTK3
 backend_tools.ToolHelp = HelpGTK3
 backend_tools.ToolCopyToClipboard = ToolCopyToClipboardGTK3
diff --git a/lib/matplotlib/backends/backend_macosx.py b/lib/matplotlib/backends/backend_macosx.py
index c84087f3b209..d4fca882bd81 100644
--- a/lib/matplotlib/backends/backend_macosx.py
+++ b/lib/matplotlib/backends/backend_macosx.py
@@ -39,6 +39,10 @@ def _set_device_scale(self, value):
             self._dpi_ratio, old_value = value, self._dpi_ratio
             self.figure.dpi = self.figure.dpi / old_value * self._dpi_ratio
 
+    def set_cursor(self, cursor):
+        # docstring inherited
+        _macosx.set_cursor(cursor)
+
     def _draw(self):
         renderer = self.get_renderer(cleared=self.figure.stale)
         if self.figure.stale:
@@ -108,9 +112,6 @@ def release_zoom(self, event):
         super().release_zoom(event)
         self.canvas.remove_rubberband()
 
-    def set_cursor(self, cursor):
-        _macosx.set_cursor(cursor)
-
     def save_figure(self, *args):
         filename = _macosx.choose_save_file('Save the figure',
                                             self.canvas.get_default_filename())
diff --git a/lib/matplotlib/backends/backend_qt5.py b/lib/matplotlib/backends/backend_qt5.py
index 0523d4d8ca7d..754604a21820 100644
--- a/lib/matplotlib/backends/backend_qt5.py
+++ b/lib/matplotlib/backends/backend_qt5.py
@@ -241,6 +241,10 @@ def showEvent(self, event):
         window.screenChanged.connect(self._update_screen)
         self._update_screen(window.screen())
 
+    def set_cursor(self, cursor):
+        # docstring inherited
+        self.setCursor(_api.check_getitem(cursord, cursor=cursor))
+
     def enterEvent(self, event):
         try:
             x, y = self.mouseEventCoords(event.pos())
@@ -702,9 +706,6 @@ def set_message(self, s):
         if self.coordinates:
             self.locLabel.setText(s)
 
-    def set_cursor(self, cursor):
-        self.canvas.setCursor(cursord[cursor])
-
     def draw_rubberband(self, event, x0, y0, x1, y1):
         height = self.canvas.figure.bbox.height
         y1 = height - y1
@@ -931,6 +932,7 @@ def trigger(self, *args):
             self._make_classic_style_pseudo_toolbar())
 
 
+@_api.deprecated("3.5", alternative="ToolSetCursor")
 class SetCursorQt(backend_tools.SetCursorBase):
     def set_cursor(self, cursor):
         NavigationToolbar2QT.set_cursor(
@@ -960,7 +962,6 @@ def trigger(self, *args, **kwargs):
 
 backend_tools.ToolSaveFigure = SaveFigureQt
 backend_tools.ToolConfigureSubplots = ConfigureSubplotsQt
-backend_tools.ToolSetCursor = SetCursorQt
 backend_tools.ToolRubberband = RubberbandQt
 backend_tools.ToolHelp = HelpQt
 backend_tools.ToolCopyToClipboard = ToolCopyToClipboardQT
diff --git a/lib/matplotlib/backends/backend_webagg_core.py b/lib/matplotlib/backends/backend_webagg_core.py
index ceb5c4be8e16..a66a9ec76cdc 100644
--- a/lib/matplotlib/backends/backend_webagg_core.py
+++ b/lib/matplotlib/backends/backend_webagg_core.py
@@ -157,6 +157,19 @@ def blit(self, bbox=None):
     def draw_idle(self):
         self.send_event("draw")
 
+    def set_cursor(self, cursor):
+        # docstring inherited
+        cursor = _api.check_getitem({
+            backend_tools.Cursors.HAND: 'pointer',
+            backend_tools.Cursors.POINTER: 'default',
+            backend_tools.Cursors.SELECT_REGION: 'crosshair',
+            backend_tools.Cursors.MOVE: 'move',
+            backend_tools.Cursors.WAIT: 'wait',
+            backend_tools.Cursors.RESIZE_HORIZONTAL: 'ew-resize',
+            backend_tools.Cursors.RESIZE_VERTICAL: 'ns-resize',
+        }, cursor=cursor)
+        self.send_event('cursor', cursor=cursor)
+
     def set_image_mode(self, mode):
         """
         Set the image mode for any subsequent images which will be sent
@@ -362,9 +375,11 @@ class NavigationToolbar2WebAgg(backend_bases.NavigationToolbar2):
         if name_of_method in _ALLOWED_TOOL_ITEMS
     ]
 
+    cursor = _api.deprecate_privatize_attribute("3.5")
+
     def __init__(self, canvas):
         self.message = ''
-        self.cursor = None
+        self._cursor = None  # Remove with deprecation.
         super().__init__(canvas)
 
     def set_message(self, message):
@@ -372,20 +387,6 @@ def set_message(self, message):
             self.canvas.send_event("message", message=message)
         self.message = message
 
-    def set_cursor(self, cursor):
-        if cursor != self.cursor:
-            cursor = {
-                backend_tools.Cursors.HAND: 'pointer',
-                backend_tools.Cursors.POINTER: 'default',
-                backend_tools.Cursors.SELECT_REGION: 'crosshair',
-                backend_tools.Cursors.MOVE: 'move',
-                backend_tools.Cursors.WAIT: 'wait',
-                backend_tools.Cursors.RESIZE_HORIZONTAL: 'ew-resize',
-                backend_tools.Cursors.RESIZE_VERTICAL: 'ns-resize',
-            }[cursor]
-            self.canvas.send_event("cursor", cursor=cursor)
-        self.cursor = cursor
-
     def draw_rubberband(self, event, x0, y0, x1, y1):
         self.canvas.send_event(
             "rubberband", x0=x0, y0=y0, x1=x1, y1=y1)
diff --git a/lib/matplotlib/backends/backend_wx.py b/lib/matplotlib/backends/backend_wx.py
index ece3db76955a..61176e434c4c 100644
--- a/lib/matplotlib/backends/backend_wx.py
+++ b/lib/matplotlib/backends/backend_wx.py
@@ -719,6 +719,12 @@ def _onKeyUp(self, event):
         if self:
             event.Skip()
 
+    def set_cursor(self, cursor):
+        # docstring inherited
+        cursor = wx.Cursor(_api.check_getitem(cursord, cursor=cursor))
+        self.SetCursor(cursor)
+        self.Update()
+
     def _set_capture(self, capture=True):
         """Control wx mouse capture."""
         if self.HasCapture():
@@ -1155,11 +1161,6 @@ def save_figure(self, *args):
             except Exception as e:
                 error_msg_wx(str(e))
 
-    def set_cursor(self, cursor):
-        cursor = wx.Cursor(cursord[cursor])
-        self.canvas.SetCursor(cursor)
-        self.canvas.Update()
-
     def draw_rubberband(self, event, x0, y0, x1, y1):
         height = self.canvas.figure.bbox.height
         self.canvas._rubberband_rect = (x0, height - y0, x1, height - y1)
@@ -1281,6 +1282,7 @@ def trigger(self, *args):
             self._make_classic_style_pseudo_toolbar())
 
 
+@_api.deprecated("3.5", alternative="ToolSetCursor")
 class SetCursorWx(backend_tools.SetCursorBase):
     def set_cursor(self, cursor):
         NavigationToolbar2Wx.set_cursor(
@@ -1362,7 +1364,6 @@ def trigger(self, *args, **kwargs):
 
 backend_tools.ToolSaveFigure = SaveFigureWx
 backend_tools.ToolConfigureSubplots = ConfigureSubplotsWx
-backend_tools.ToolSetCursor = SetCursorWx
 backend_tools.ToolRubberband = RubberbandWx
 backend_tools.ToolHelp = HelpWx
 backend_tools.ToolCopyToClipboard = ToolCopyToClipboardWx