diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index b006d3820889f..5e8d2c9c39259 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -771,6 +771,11 @@ Other API changes
   or :attr:`~DataFrame.iloc` (thus, ``df.loc[:, :]`` or ``df.iloc[:, :]``) now returns a
   new DataFrame (shallow copy) instead of the original DataFrame, consistent with other
   methods to get a full slice (for example ``df.loc[:]`` or ``df[:]``) (:issue:`49469`)
+- The :class:`Series` and :class:`DataFrame` constructors will now return a shallow copy
+  (i.e. share data, but not attributes) when passed a Series and DataFrame,
+  respectively, and with the default of ``copy=False`` (and if no other keyword triggers
+  a copy). Previously, the new Series or DataFrame would share the index attribute (e.g.
+  ``df.index = ...`` would also update the index of the parent or child) (:issue:`49523`)
 - Disallow computing ``cumprod`` for :class:`Timedelta` object; previously this returned incorrect values (:issue:`50246`)
 - :class:`DataFrame` objects read from a :class:`HDFStore` file without an index now have a :class:`RangeIndex` instead of an ``int64`` index (:issue:`51076`)
 - Instantiating an :class:`Index` with an numeric numpy dtype with data containing :class:`NA` and/or :class:`NaT` now raises a ``ValueError``. Previously a ``TypeError`` was raised (:issue:`51050`)
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 2361c254f5161..2650090a3f61a 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -652,6 +652,10 @@ def __init__(
 
         if isinstance(data, DataFrame):
             data = data._mgr
+            if not copy:
+                # if not copying data, ensure to still return a shallow copy
+                # to avoid the result sharing the same Manager
+                data = data.copy(deep=False)
 
         if isinstance(data, (BlockManager, ArrayManager)):
             # first check if a Manager is passed without any other arguments
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 80dd0dd19f96f..34d18b779c71b 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -446,10 +446,7 @@ def __init__(
         elif isinstance(data, Series):
             if index is None:
                 index = data.index
-                if using_copy_on_write():
-                    data = data._mgr.copy(deep=False)
-                else:
-                    data = data._mgr
+                data = data._mgr.copy(deep=False)
             else:
                 data = data.reindex(index, copy=copy)
                 copy = False
diff --git a/pandas/tests/frame/test_constructors.py b/pandas/tests/frame/test_constructors.py
index c621e9bae78f8..d4d2164f2a4a7 100644
--- a/pandas/tests/frame/test_constructors.py
+++ b/pandas/tests/frame/test_constructors.py
@@ -285,10 +285,8 @@ def test_constructor_dtype_nocast_view_dataframe(self, using_copy_on_write):
         df = DataFrame([[1, 2]])
         should_be_view = DataFrame(df, dtype=df[0].dtype)
         if using_copy_on_write:
-            # TODO(CoW) doesn't mutate original
             should_be_view.iloc[0, 0] = 99
-            # assert df.values[0, 0] == 1
-            assert df.values[0, 0] == 99
+            assert df.values[0, 0] == 1
         else:
             should_be_view[0][0] = 99
             assert df.values[0, 0] == 99
@@ -2100,6 +2098,17 @@ def test_constructor_frame_copy(self, float_frame):
         assert (cop["A"] == 5).all()
         assert not (float_frame["A"] == 5).all()
 
+    def test_constructor_frame_shallow_copy(self, float_frame):
+        # constructing a DataFrame from DataFrame with copy=False should still
+        # give a "shallow" copy (share data, not attributes)
+        # https://github.com/pandas-dev/pandas/issues/49523
+        orig = float_frame.copy()
+        cop = DataFrame(float_frame)
+        assert cop._mgr is not float_frame._mgr
+        # Overwriting index of copy doesn't change original
+        cop.index = np.arange(len(cop))
+        tm.assert_frame_equal(float_frame, orig)
+
     def test_constructor_ndarray_copy(self, float_frame, using_array_manager):
         if not using_array_manager:
             df = DataFrame(float_frame.values)
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index 2d85462691896..951c9df0f6e99 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -727,6 +727,18 @@ def test_constructor_limit_copies(self, index):
         # we make 1 copy; this is just a smoke test here
         assert s._mgr.blocks[0].values is not index
 
+    def test_constructor_shallow_copy(self):
+        # constructing a Series from Series with copy=False should still
+        # give a "shallow" copy (share data, not attributes)
+        # https://github.com/pandas-dev/pandas/issues/49523
+        s = Series([1, 2, 3])
+        s_orig = s.copy()
+        s2 = Series(s)
+        assert s2._mgr is not s._mgr
+        # Overwriting index of s2 doesn't change s
+        s2.index = ["a", "b", "c"]
+        tm.assert_series_equal(s, s_orig)
+
     def test_constructor_pass_none(self):
         s = Series(None, index=range(5))
         assert s.dtype == np.float64