diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 8980fe0249193..2164163632cb1 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -160,7 +160,10 @@
     BlockManager,
     SingleArrayManager,
 )
-from pandas.core.internals.construction import mgr_to_mgr
+from pandas.core.internals.construction import (
+    mgr_to_mgr,
+    ndarray_to_mgr,
+)
 from pandas.core.methods.describe import describe_ndframe
 from pandas.core.missing import (
     clean_fill_method,
@@ -763,7 +766,7 @@ def _set_axis(self, axis: AxisInt, labels: AnyArrayLike | list) -> None:
 
     @final
     def swapaxes(
-        self: NDFrameT, axis1: Axis, axis2: Axis, copy: bool_t = True
+        self: NDFrameT, axis1: Axis, axis2: Axis, copy: bool_t | None = None
     ) -> NDFrameT:
         """
         Interchange axes and swap values axes appropriately.
@@ -776,15 +779,36 @@ def swapaxes(
         j = self._get_axis_number(axis2)
 
         if i == j:
-            if copy:
-                return self.copy()
-            return self
+            if copy is False and not using_copy_on_write():
+                return self
+            return self.copy(deep=copy)
 
         mapping = {i: j, j: i}
 
-        new_axes = (self._get_axis(mapping.get(k, k)) for k in range(self._AXIS_LEN))
+        new_axes = [self._get_axis(mapping.get(k, k)) for k in range(self._AXIS_LEN)]
         new_values = self.values.swapaxes(i, j)
-        if copy:
+        if (
+            using_copy_on_write()
+            and self._mgr.is_single_block
+            and isinstance(self._mgr, BlockManager)
+        ):
+            # This should only get hit in case of having a single block, otherwise a
+            # copy is made, we don't have to set up references.
+            new_mgr = ndarray_to_mgr(
+                new_values,
+                new_axes[0],
+                new_axes[1],
+                dtype=None,
+                copy=False,
+                typ="block",
+            )
+            assert isinstance(new_mgr, BlockManager)
+            assert isinstance(self._mgr, BlockManager)
+            new_mgr.parent = self._mgr
+            new_mgr.refs = [weakref.ref(self._mgr.blocks[0])]
+            return self._constructor(new_mgr).__finalize__(self, method="swapaxes")
+
+        elif (copy or copy is None) and self._mgr.is_single_block:
             new_values = new_values.copy()
 
         return self._constructor(
diff --git a/pandas/tests/copy_view/test_methods.py b/pandas/tests/copy_view/test_methods.py
index 2bc4202cce5f5..d221d617932e5 100644
--- a/pandas/tests/copy_view/test_methods.py
+++ b/pandas/tests/copy_view/test_methods.py
@@ -346,6 +346,41 @@ def test_to_frame(using_copy_on_write):
         tm.assert_frame_equal(df, expected)
 
 
+@pytest.mark.parametrize("ax", ["index", "columns"])
+def test_swapaxes_noop(using_copy_on_write, ax):
+    df = DataFrame({"a": [1, 2, 3], "b": [4, 5, 6]})
+    df_orig = df.copy()
+    df2 = df.swapaxes(ax, ax)
+
+    if using_copy_on_write:
+        assert np.shares_memory(get_array(df2, "a"), get_array(df, "a"))
+    else:
+        assert not np.shares_memory(get_array(df2, "a"), get_array(df, "a"))
+
+    # mutating df2 triggers a copy-on-write for that column/block
+    df2.iloc[0, 0] = 0
+    if using_copy_on_write:
+        assert not np.shares_memory(get_array(df2, "a"), get_array(df, "a"))
+    tm.assert_frame_equal(df, df_orig)
+
+
+def test_swapaxes_single_block(using_copy_on_write):
+    df = DataFrame({"a": [1, 2, 3], "b": [4, 5, 6]}, index=["x", "y", "z"])
+    df_orig = df.copy()
+    df2 = df.swapaxes("index", "columns")
+
+    if using_copy_on_write:
+        assert np.shares_memory(get_array(df2, "x"), get_array(df, "a"))
+    else:
+        assert not np.shares_memory(get_array(df2, "x"), get_array(df, "a"))
+
+    # mutating df2 triggers a copy-on-write for that column/block
+    df2.iloc[0, 0] = 0
+    if using_copy_on_write:
+        assert not np.shares_memory(get_array(df2, "x"), get_array(df, "a"))
+    tm.assert_frame_equal(df, df_orig)
+
+
 @pytest.mark.parametrize(
     "method, idx",
     [