diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 752d08a526d8c..26a9a6854b8c5 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -1275,6 +1275,7 @@ Other
 - Bug in ``divmod`` and ``rdivmod`` with :class:`DataFrame`, :class:`Series`, and :class:`Index` with ``bool`` dtypes failing to raise, which was inconsistent with ``__floordiv__`` behavior (:issue:`46043`)
 - Bug in printing a :class:`DataFrame` with a :class:`DataFrame` stored in :attr:`DataFrame.attrs` raised a ``ValueError`` (:issue:`60455`)
 - Bug in printing a :class:`Series` with a :class:`DataFrame` stored in :attr:`Series.attrs` raised a ``ValueError`` (:issue:`60568`)
+- Bug when calling :py:func:`copy.copy` on a :class:`DataFrame` or :class:`Series` which would return a deep copy instead of a shallow copy (:issue:`62971`)
 - Deprecated the keyword ``check_datetimelike_compat`` in :meth:`testing.assert_frame_equal` and :meth:`testing.assert_series_equal` (:issue:`55638`)
 - Fixed bug in :meth:`Series.replace` and :meth:`DataFrame.replace` when trying to replace :class:`NA` values in a :class:`Float64Dtype` object with ``np.nan``; this now works with ``pd.set_option("mode.nan_is_na", False)`` and is irrelevant otherwise (:issue:`55127`)
 - Fixed bug in :meth:`Series.replace` and :meth:`DataFrame.replace` when trying to replace :class:`np.nan` values in a :class:`Int64Dtype` object with :class:`NA`; this is now a no-op with ``pd.set_option("mode.nan_is_na", False)`` and is irrelevant otherwise (:issue:`51237`)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index b542ca1f431c3..735a59e5cfbb8 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -6680,8 +6680,8 @@ def copy(self, deep: bool = True) -> Self:
         )
 
     @final
-    def __copy__(self, deep: bool = True) -> Self:
-        return self.copy(deep=deep)
+    def __copy__(self) -> Self:
+        return self.copy(deep=False)
 
     @final
     def __deepcopy__(self, memo=None) -> Self:
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 72f7a1e086b60..904de6a012671 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -1413,8 +1413,8 @@ def copy(
         return new_index
 
     @final
-    def __copy__(self, **kwargs) -> Self:
-        return self.copy(**kwargs)
+    def __copy__(self) -> Self:
+        return self.copy(deep=False)
 
     @final
     def __deepcopy__(self, memo=None) -> Self:
diff --git a/pandas/tests/generic/test_generic.py b/pandas/tests/generic/test_generic.py
index b591b1b1092d4..ee6503b6929b6 100644
--- a/pandas/tests/generic/test_generic.py
+++ b/pandas/tests/generic/test_generic.py
@@ -307,6 +307,11 @@ def test_copy_and_deepcopy(self, frame_or_series, shape, func):
         assert obj_copy is not obj
         tm.assert_equal(obj_copy, obj)
 
+    def test_stdlib_copy_shallow_copies(self, frame_or_series):
+        obj = frame_or_series(range(3))
+        obj_copy = copy(obj)
+        assert tm.shares_memory(obj, obj_copy)
+
 
 class TestNDFrame:
     # tests that don't fit elsewhere