diff --git a/doc/source/whatsnew/v0.24.0.rst b/doc/source/whatsnew/v0.24.0.rst
index 98941b6d353bb..b614d760c7b7d 100644
--- a/doc/source/whatsnew/v0.24.0.rst
+++ b/doc/source/whatsnew/v0.24.0.rst
@@ -1303,6 +1303,7 @@ Indexing
 - Bug where setting a timedelta column by ``Index`` causes it to be casted to double, and therefore lose precision (:issue:`23511`)
 - Bug in :func:`Index.union` and :func:`Index.intersection` where name of the ``Index`` of the result was not computed correctly for certain cases (:issue:`9943`, :issue:`9862`)
 - Bug in :class:`Index` slicing with boolean :class:`Index` may raise ``TypeError`` (:issue:`22533`)
+- Bug when :class:`Series` was created from :class:`DatetimeIndex`, the series shares the same data with that index (:issue:`21907`)
 
 Missing
 ^^^^^^^
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 892b24f6ee552..9ecb4b52bbb46 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -181,8 +181,11 @@ def __init__(self, data=None, index=None, dtype=None, name=None,
                     # astype copies
                     data = data.astype(dtype)
                 else:
-                    # need to copy to avoid aliasing issues
-                    data = data._values.copy()
+                    # GH21907
+                    if isinstance(data._values, DatetimeIndex):
+                        data = data.copy(deep=True)
+                    else:
+                        data = data._values.copy()
                 copy = False
 
             elif isinstance(data, np.ndarray):
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index ce0cf0d5c089e..8106fa8125103 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -970,6 +970,24 @@ def test_constructor_set(self):
         values = frozenset(values)
         pytest.raises(TypeError, Series, values)
 
+    @pytest.mark.parametrize(
+        "src",
+        [pd.date_range('2016-01-01', periods=10, tz='US/Pacific'),
+         pd.timedelta_range('1 day', periods=10),
+         pd.period_range('2012Q1', periods=3, freq='Q'),
+         pd.Index(list('abcdefghij')),
+         pd.Int64Index(np.arange(10)),
+         pd.RangeIndex(0, 10)])
+    def test_fromIndex(self, src):
+        # GH21907
+        # When constructing a series from an index,
+        # the series does not share data with that index
+        expected = src.copy(deep=True)
+        prod = Series(src)
+        prod[::3] = NaT
+        assert expected[0] is not NaT
+        tm.assert_index_equal(src, expected)
+
     # https://github.com/pandas-dev/pandas/issues/22698
     @pytest.mark.filterwarnings("ignore:elementwise comparison:FutureWarning")
     def test_fromDict(self):