diff --git a/doc/api/next_api_changes/deprecations/20995-AL.rst b/doc/api/next_api_changes/deprecations/20995-AL.rst
new file mode 100644
index 000000000000..bdccd8f5d333
--- /dev/null
+++ b/doc/api/next_api_changes/deprecations/20995-AL.rst
@@ -0,0 +1,3 @@
+``backend_gtk3.icon_filename`` and ``backend_gtk3.window_icon``
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+... are deprecated with no replacement.
diff --git a/lib/matplotlib/backends/backend_gtk3.py b/lib/matplotlib/backends/backend_gtk3.py
index 7701d7742bf0..efbbbb387238 100644
--- a/lib/matplotlib/backends/backend_gtk3.py
+++ b/lib/matplotlib/backends/backend_gtk3.py
@@ -59,6 +59,13 @@ def cursord(self):
         except TypeError as exc:
             return {}
 
+    icon_filename = _api.deprecated("3.6", obj_type="")(property(
+        lambda self:
+        "matplotlib.png" if sys.platform == "win32" else "matplotlib.svg"))
+    window_icon = _api.deprecated("3.6", obj_type="")(property(
+        lambda self:
+        str(cbook._get_data_path("images", __getattr__("icon_filename")))))
+
 
 @functools.lru_cache()
 def _mpl_to_gtk_cursor(mpl_cursor):
@@ -307,7 +314,9 @@ def __init__(self, canvas, num):
         super().__init__(canvas, num)
 
         self.window.set_wmclass("matplotlib", "Matplotlib")
-        self.window.set_icon_from_file(window_icon)
+        icon_ext = "png" if sys.platform == "win32" else "svg"
+        self.window.set_icon_from_file(
+            str(cbook._get_data_path(f"images/matplotlib.{icon_ext}")))
 
         self.vbox = Gtk.Box()
         self.vbox.set_property("orientation", Gtk.Orientation.VERTICAL)
@@ -698,14 +707,6 @@ def trigger(self, *args, **kwargs):
         clipboard.set_image(pb)
 
 
-# Define the file to use as the GTk icon
-if sys.platform == 'win32':
-    icon_filename = 'matplotlib.png'
-else:
-    icon_filename = 'matplotlib.svg'
-window_icon = str(cbook._get_data_path('images', icon_filename))
-
-
 def error_msg_gtk(msg, parent=None):
     if parent is not None:  # find the toplevel Gtk.Window
         parent = parent.get_toplevel()