diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 8980fe0249193..fa1a79c81630a 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -35,6 +35,7 @@
 )
 
 from pandas._libs import lib
+from pandas._libs.lib import array_equal_fast
 from pandas._libs.tslibs import (
     Period,
     Tick,
@@ -3754,6 +3755,18 @@ def _take(
 
         See the docstring of `take` for full explanation of the parameters.
         """
+        if not isinstance(indices, slice):
+            indices = np.asarray(indices, dtype=np.intp)
+            if (
+                axis == 0
+                and indices.ndim == 1
+                and using_copy_on_write()
+                and array_equal_fast(
+                    indices,
+                    np.arange(0, len(self), dtype=np.intp),
+                )
+            ):
+                return self.copy(deep=None)
 
         new_data = self._mgr.take(
             indices,
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 6b82d48f82ce7..c38eb4e7c5d34 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -32,7 +32,10 @@
     properties,
     reshape,
 )
-from pandas._libs.lib import no_default
+from pandas._libs.lib import (
+    array_equal_fast,
+    no_default,
+)
 from pandas._typing import (
     AggFuncType,
     AlignJoin,
@@ -879,6 +882,14 @@ def take(self, indices, axis: Axis = 0, **kwargs) -> Series:
         nv.validate_take((), kwargs)
 
         indices = ensure_platform_int(indices)
+
+        if (
+            indices.ndim == 1
+            and using_copy_on_write()
+            and array_equal_fast(indices, np.arange(0, len(self), dtype=indices.dtype))
+        ):
+            return self.copy(deep=None)
+
         new_index = self.index.take(indices)
         new_values = self._values.take(indices)
 
diff --git a/pandas/tests/copy_view/test_methods.py b/pandas/tests/copy_view/test_methods.py
index 2bc4202cce5f5..67bf9a117f2a0 100644
--- a/pandas/tests/copy_view/test_methods.py
+++ b/pandas/tests/copy_view/test_methods.py
@@ -540,6 +540,40 @@ def test_assign_drop_duplicates(using_copy_on_write, method):
     tm.assert_frame_equal(df, df_orig)
 
 
+@pytest.mark.parametrize("obj", [Series([1, 2]), DataFrame({"a": [1, 2]})])
+def test_take(using_copy_on_write, obj):
+    # Check that no copy is made when we take all rows in original order
+    obj_orig = obj.copy()
+    obj2 = obj.take([0, 1])
+
+    if using_copy_on_write:
+        assert np.shares_memory(obj2.values, obj.values)
+    else:
+        assert not np.shares_memory(obj2.values, obj.values)
+
+    obj2.iloc[0] = 0
+    if using_copy_on_write:
+        assert not np.shares_memory(obj2.values, obj.values)
+    tm.assert_equal(obj, obj_orig)
+
+
+@pytest.mark.parametrize("obj", [Series([1, 2]), DataFrame({"a": [1, 2]})])
+def test_between_time(using_copy_on_write, obj):
+    obj.index = date_range("2018-04-09", periods=2, freq="1D20min")
+    obj_orig = obj.copy()
+    obj2 = obj.between_time("0:00", "1:00")
+
+    if using_copy_on_write:
+        assert np.shares_memory(obj2.values, obj.values)
+    else:
+        assert not np.shares_memory(obj2.values, obj.values)
+
+    obj2.iloc[0] = 0
+    if using_copy_on_write:
+        assert not np.shares_memory(obj2.values, obj.values)
+    tm.assert_equal(obj, obj_orig)
+
+
 def test_reindex_like(using_copy_on_write):
     df = DataFrame({"a": [1, 2], "b": "a"})
     other = DataFrame({"b": "a", "a": [1, 2]})