diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 2abab547ff95..7c9b12d3ced3 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -647,7 +647,7 @@ def __init__(self, fig,
             args = (rect,)
         subplotspec = None
         if len(args) == 1 and isinstance(args[0], mtransforms.Bbox):
-            self._position = args[0]
+            self._position = args[0].frozen()
         elif len(args) == 1 and np.iterable(args[0]):
             self._position = mtransforms.Bbox.from_bounds(*args[0])
         else:
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index beac9850539e..854068d0d03c 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -9581,3 +9581,14 @@ def test_bar_color_precedence():
     bars = ax.bar([31, 32, 33], [4, 5, 6], color='red', facecolor='green')
     for bar in bars:
         assert mcolors.same_color(bar.get_facecolor(), 'green')
+
+
+@check_figures_equal(extensions=['png'])
+def test_axes_set_position_external_bbox_unchanged(fig_test, fig_ref):
+    # From #29410: Modifying Axes' position also alters the original Bbox
+    # object used for initialization
+    bbox = mtransforms.Bbox([[0.0, 0.0], [1.0, 1.0]])
+    ax_test = fig_test.add_axes(bbox)
+    ax_test.set_position([0.25, 0.25, 0.5, 0.5])
+    assert (bbox.x0, bbox.y0, bbox.width, bbox.height) == (0.0, 0.0, 1.0, 1.0)
+    ax_ref = fig_ref.add_axes([0.25, 0.25, 0.5, 0.5])