diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 9534eca51f383..6e2fd68b60a54 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -740,7 +740,8 @@ def _set_axis_nocheck(self, labels, axis: Axis, inplace: bool_t, copy: bool_t):
         else:
             # With copy=False, we create a new object but don't copy the
             #  underlying data.
-            obj = self.copy(deep=copy)
+            if copy:
+                obj = self.copy(deep=None)
             setattr(obj, obj._get_axis_name(axis), labels)
             return obj
 
diff --git a/pandas/tests/copy_view/test_methods.py b/pandas/tests/copy_view/test_methods.py
index f5c7b31e59bc5..4d0a225086e5d 100644
--- a/pandas/tests/copy_view/test_methods.py
+++ b/pandas/tests/copy_view/test_methods.py
@@ -321,6 +321,21 @@ def test_head_tail(method, using_copy_on_write):
         df2.iloc[0, 0] = 1
     tm.assert_frame_equal(df, df_orig)
 
+def test_droplevel(using_copy_on_write):
+    # GH 49473
+    df = DataFrame({"a": [1, 2, 3], "b": [4, 5, 6], "c": [7, 8, 9]}).set_index(["a","b"])   
+    df_orig = df.copy()
+    df2 = df.droplevel(0) 
+    
+    if using_copy_on_write:
+        assert np.shares_memory(get_array(df2, "c"), get_array(df, "c"))
+    else:
+        assert not np.shares_memory(get_array(df2, "c"), get_array(df, "c"))
+
+    # mutating df2 triggers a copy-on-write for that column / block
+    df2.loc["b","c"] = 1
+    
+
 
 def test_assign(using_copy_on_write):
     df = DataFrame({"a": [1, 2, 3]})
@@ -356,3 +371,6 @@ def test_reorder_levels(using_copy_on_write):
     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)
+
+    assert not np.shares_memory(get_array(df2, "c"), get_array(df, "c"))
+    tm.assert_frame_equal(df, df_orig)