diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 5b77bb9651073..de99effdfe579 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -750,7 +750,7 @@ def swapaxes(
         mapping = {i: j, j: i}
 
         new_axes = [self._get_axis(mapping.get(k, k)) for k in range(self._AXIS_LEN)]
-        new_values = self.values.swapaxes(i, j)
+        new_values = self._values.swapaxes(i, j)  # type: ignore[union-attr]
         if (
             using_copy_on_write()
             and self._mgr.is_single_block
diff --git a/pandas/tests/copy_view/test_methods.py b/pandas/tests/copy_view/test_methods.py
index 399c7cbef2009..cd49763bc2186 100644
--- a/pandas/tests/copy_view/test_methods.py
+++ b/pandas/tests/copy_view/test_methods.py
@@ -641,6 +641,14 @@ def test_swapaxes_single_block(using_copy_on_write):
     tm.assert_frame_equal(df, df_orig)
 
 
+def test_swapaxes_read_only_array():
+    df = DataFrame({"a": [1, 2], "b": 3})
+    df = df.swapaxes(axis1="index", axis2="columns")
+    df.iloc[0, 0] = 100
+    expected = DataFrame({0: [100, 3], 1: [2, 3]}, index=["a", "b"])
+    tm.assert_frame_equal(df, expected)
+
+
 @pytest.mark.parametrize(
     "method, idx",
     [