diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index a8631f42fb2d6..00a03f6e4619f 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -5855,7 +5855,8 @@ def set_index(
         if inplace:
             frame = self
         else:
-            frame = self.copy()
+            # GH 49473 Use "lazy copy" with Copy-on-Write
+            frame = self.copy(deep=None)
 
         arrays = []
         names: list[Hashable] = []
diff --git a/pandas/tests/copy_view/test_methods.py b/pandas/tests/copy_view/test_methods.py
index 956e2cf98c9b6..9488211e2a0e6 100644
--- a/pandas/tests/copy_view/test_methods.py
+++ b/pandas/tests/copy_view/test_methods.py
@@ -214,3 +214,20 @@ def test_chained_methods(request, method, idx, using_copy_on_write):
     df.iloc[0, 0] = 0
     if not df2_is_view:
         tm.assert_frame_equal(df2.iloc[:, idx:], df_orig)
+
+
+def test_set_index(using_copy_on_write):
+    # GH 49473
+    df = DataFrame({"a": [1, 2, 3], "b": [4, 5, 6], "c": [0.1, 0.2, 0.3]})
+    df_orig = df.copy()
+    df2 = df.set_index("a")
+
+    if using_copy_on_write:
+        assert np.shares_memory(get_array(df2, "b"), get_array(df, "b"))
+    else:
+        assert not np.shares_memory(get_array(df2, "b"), get_array(df, "b"))
+
+    # mutating df2 triggers a copy-on-write for that column / block
+    df2.iloc[0, 1] = 0
+    assert not np.shares_memory(get_array(df2, "c"), get_array(df, "c"))
+    tm.assert_frame_equal(df, df_orig)