diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index bf79e58077179..f5164abb06ae2 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -4831,6 +4831,8 @@ def _reindex_axes(
                 copy=copy,
                 allow_dups=False,
             )
+            # If we've made a copy once, no need to make another one
+            copy = False
 
         return obj
 
diff --git a/pandas/core/internals/array_manager.py b/pandas/core/internals/array_manager.py
index bd049b80b281c..f215cc656b1d3 100644
--- a/pandas/core/internals/array_manager.py
+++ b/pandas/core/internals/array_manager.py
@@ -610,6 +610,8 @@ def _reindex_indexer(
                     )
                 else:
                     arr = self.arrays[i]
+                    if copy:
+                        arr = arr.copy()
                 new_arrays.append(arr)
 
         else:
diff --git a/pandas/tests/frame/methods/test_reindex.py b/pandas/tests/frame/methods/test_reindex.py
index d0765084adfa9..6b73c6a662da7 100644
--- a/pandas/tests/frame/methods/test_reindex.py
+++ b/pandas/tests/frame/methods/test_reindex.py
@@ -83,6 +83,20 @@ class TestDataFrameSelectReindex:
     # These are specific reindex-based tests; other indexing tests should go in
     # test_indexing
 
+    def test_reindex_copies(self):
+        # based on asv time_reindex_axis1
+        N = 10
+        df = DataFrame(np.random.randn(N * 10, N))
+        cols = np.arange(N)
+        np.random.shuffle(cols)
+
+        result = df.reindex(columns=cols, copy=True)
+        assert not np.shares_memory(result[0]._values, df[0]._values)
+
+        # pass both columns and index
+        result2 = df.reindex(columns=cols, index=df.index, copy=True)
+        assert not np.shares_memory(result2[0]._values, df[0]._values)
+
     def test_reindex_date_fill_value(self):
         # passing date to dt64 is deprecated
         arr = date_range("2016-01-01", periods=6).values.reshape(3, 2)