diff --git a/doc/api/next_api_changes/deprecations/19763-ES.rst b/doc/api/next_api_changes/deprecations/19763-ES.rst
new file mode 100644
index 000000000000..6df1b0abaa75
--- /dev/null
+++ b/doc/api/next_api_changes/deprecations/19763-ES.rst
@@ -0,0 +1,5 @@
+``Cursor`` and ``MultiCursor`` event handlers are now private
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Access to the event handlers for the `.Cursor` and `.MultiCursor` widgets is
+now deprecated.
diff --git a/lib/matplotlib/tests/test_widgets.py b/lib/matplotlib/tests/test_widgets.py
index 4e1455660da9..f09c7ab4b3b6 100644
--- a/lib/matplotlib/tests/test_widgets.py
+++ b/lib/matplotlib/tests/test_widgets.py
@@ -1517,7 +1517,7 @@ def test_MultiCursor(horizOn, vertOn):
     # Can't use `do_event` as that helper requires the widget
     # to have a single .ax attribute.
     event = mock_event(ax1, xdata=.5, ydata=.25)
-    multi.onmove(event)
+    multi._onmove(event)
 
     # the lines in the first two ax should both move
     for l in multi.vlines:
@@ -1528,7 +1528,7 @@ def test_MultiCursor(horizOn, vertOn):
     # test a move event in an Axes not part of the MultiCursor
     # the lines in ax1 and ax2 should not have moved.
     event = mock_event(ax3, xdata=.75, ydata=.75)
-    multi.onmove(event)
+    multi._onmove(event)
     for l in multi.vlines:
         assert l.get_xdata() == (.5, .5)
     for l in multi.hlines:
diff --git a/lib/matplotlib/widgets.py b/lib/matplotlib/widgets.py
index 24a5bcad98d5..a909b856951e 100644
--- a/lib/matplotlib/widgets.py
+++ b/lib/matplotlib/widgets.py
@@ -1600,8 +1600,8 @@ def __init__(self, ax, horizOn=True, vertOn=True, useblit=False,
                  **lineprops):
         super().__init__(ax)
 
-        self.connect_event('motion_notify_event', self.onmove)
-        self.connect_event('draw_event', self.clear)
+        self.connect_event('motion_notify_event', self._onmove)
+        self.connect_event('draw_event', self._clear)
 
         self.visible = True
         self.horizOn = horizOn
@@ -1616,16 +1616,25 @@ def __init__(self, ax, horizOn=True, vertOn=True, useblit=False,
         self.background = None
         self.needclear = False
 
+    @_api.deprecated('3.5')
     def clear(self, event):
         """Internal event handler to clear the cursor."""
+        self._clear(event)
         if self.ignore(event):
             return
-        if self.useblit:
-            self.background = self.canvas.copy_from_bbox(self.ax.bbox)
         self.linev.set_visible(False)
         self.lineh.set_visible(False)
 
-    def onmove(self, event):
+    def _clear(self, event):
+        """Internal event handler to clear the cursor."""
+        if self.ignore(event):
+            return
+        if self.useblit:
+            self.background = self.canvas.copy_from_bbox(self.ax.bbox)
+
+    onmove = _api.deprecate_privatize_attribute('3.5')
+
+    def _onmove(self, event):
         """Internal event handler to draw the cursor when the mouse moves."""
         if self.ignore(event):
             return
@@ -1640,15 +1649,15 @@ def onmove(self, event):
                 self.needclear = False
             return
         self.needclear = True
-        if not self.visible:
-            return
+
         self.linev.set_xdata((event.xdata, event.xdata))
+        self.linev.set_visible(self.visible and self.vertOn)
 
         self.lineh.set_ydata((event.ydata, event.ydata))
-        self.linev.set_visible(self.visible and self.vertOn)
         self.lineh.set_visible(self.visible and self.horizOn)
 
-        self._update()
+        if self.visible and (self.vertOn or self.horizOn):
+            self._update()
 
     def _update(self):
         if self.useblit:
@@ -1749,8 +1758,8 @@ def connect(self):
         """Connect events."""
         for canvas, info in self._canvas_infos.items():
             info["cids"] = [
-                canvas.mpl_connect('motion_notify_event', self.onmove),
-                canvas.mpl_connect('draw_event', self.clear),
+                canvas.mpl_connect('motion_notify_event', self._onmove),
+                canvas.mpl_connect('draw_event', self._clear),
             ]
 
     def disconnect(self):
@@ -1760,24 +1769,31 @@ def disconnect(self):
                 canvas.mpl_disconnect(cid)
             info["cids"].clear()
 
+    @_api.deprecated('3.5')
     def clear(self, event):
+        """Clear the cursor."""
+        if self.ignore(event):
+            return
+        self._clear(event)
+        for line in self.vlines + self.hlines:
+            line.set_visible(False)
+
+    def _clear(self, event):
         """Clear the cursor."""
         if self.ignore(event):
             return
         if self.useblit:
             for canvas, info in self._canvas_infos.items():
                 info["background"] = canvas.copy_from_bbox(canvas.figure.bbox)
-        for line in self.vlines + self.hlines:
-            line.set_visible(False)
 
-    def onmove(self, event):
+    onmove = _api.deprecate_privatize_attribute('3.5')
+
+    def _onmove(self, event):
         if (self.ignore(event)
                 or event.inaxes not in self.axes
                 or not event.canvas.widgetlock.available(self)):
             return
         self.needclear = True
-        if not self.visible:
-            return
         if self.vertOn:
             for line in self.vlines:
                 line.set_xdata((event.xdata, event.xdata))
@@ -1786,7 +1802,8 @@ def onmove(self, event):
             for line in self.hlines:
                 line.set_ydata((event.ydata, event.ydata))
                 line.set_visible(self.visible)
-        self._update()
+        if self.visible and (self.vertOn or self.horizOn):
+            self._update()
 
     def _update(self):
         if self.useblit: