diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 8fc9e3e3cf4d..12ac19a5d7c8 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -1302,9 +1302,14 @@ def __clear(self):
         self._get_patches_for_fill = _process_plot_var_args('fill')
 
         self._gridOn = mpl.rcParams['axes.grid']
+        # Swap children to minimize time we spend in an invalid state
         old_children, self._children = self._children, []
         for chld in old_children:
-            chld.axes = chld._parent_figure = None
+            chld._remove_method = None
+            chld._parent_figure = None
+            chld.axes = None
+        # Use list.clear to break the `artist._remove_method` reference cycle
+        old_children.clear()
         self._mouseover_set = _OrderedSet()
         self.child_axes = []
         self._current_image = None  # strictly for pyplot via _sci, _gci
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 5d50df4ffd20..39adfb1c445e 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -1,12 +1,14 @@
 import contextlib
-from collections import namedtuple
+from collections import namedtuple, deque
 import datetime
 from decimal import Decimal
 from functools import partial
+import gc
 import inspect
 import io
 from itertools import product
 import platform
+import sys
 from types import SimpleNamespace
 
 import dateutil.tz
@@ -23,6 +25,8 @@
 import matplotlib.dates as mdates
 from matplotlib.figure import Figure
 from matplotlib.axes import Axes
+from matplotlib.lines import Line2D
+from matplotlib.collections import PathCollection
 import matplotlib.font_manager as mfont_manager
 import matplotlib.markers as mmarkers
 import matplotlib.patches as mpatches
@@ -9209,6 +9213,49 @@ def test_axes_clear_behavior(fig_ref, fig_test, which):
     ax_test.grid(True)
 
 
+@pytest.mark.skipif(
+    sys.version_info[:3] == (3, 13, 0) and sys.version_info.releaselevel != "final",
+    reason="https://github.com/python/cpython/issues/124538",
+)
+def test_axes_clear_reference_cycle():
+    def assert_not_in_reference_cycle(start):
+        # Breadth first search. Return True if we encounter the starting node
+        to_visit = deque([start])
+        explored = set()
+        while len(to_visit) > 0:
+            parent = to_visit.popleft()
+            for child in gc.get_referents(parent):
+                if id(child) in explored:
+                    continue
+                assert child is not start
+                explored.add(id(child))
+                to_visit.append(child)
+
+    fig = Figure()
+    ax = fig.add_subplot()
+    points = np.random.rand(1000)
+    ax.plot(points, points)
+    ax.scatter(points, points)
+    ax_children = ax.get_children()
+    fig.clear()  # This should break the reference cycle
+
+    # Care most about the objects that scale with number of points
+    big_artists = [
+        a for a in ax_children
+        if isinstance(a, (Line2D, PathCollection))
+    ]
+    assert len(big_artists) > 0
+    for big_artist in big_artists:
+        assert_not_in_reference_cycle(big_artist)
+    assert len(ax_children) > 0
+    for child in ax_children:
+        # Make sure this doesn't raise because the child is already removed.
+        try:
+            child.remove()
+        except NotImplementedError:
+            pass  # not implemented is expected for some artists
+
+
 def test_boxplot_tick_labels():
     # Test the renamed `tick_labels` parameter.
     # Test for deprecation of old name `labels`.