diff --git a/doc/source/whatsnew/v1.1.5.rst b/doc/source/whatsnew/v1.1.5.rst
index 7164830392f35..cfdeeb61d8f61 100644
--- a/doc/source/whatsnew/v1.1.5.rst
+++ b/doc/source/whatsnew/v1.1.5.rst
@@ -20,6 +20,7 @@ Fixed regressions
 - Fixed regression in inplace operations on :class:`Series` with ``ExtensionDtype`` with NumPy dtyped operand (:issue:`37910`)
 - Fixed regression in metadata propagation for ``groupby`` iterator (:issue:`37343`)
 - Fixed regression in :class:`MultiIndex` constructed from a :class:`DatetimeIndex` not retaining frequency (:issue:`35563`)
+- Fixed regression in :class:`Index` constructor raising a ``AttributeError`` when passed a :class:`SparseArray` with datetime64 values (:issue:`35843`)
 - Fixed regression in :meth:`DataFrame.unstack` with columns with integer dtype (:issue:`37115`)
 - Fixed regression in indexing on a :class:`Series` with ``CategoricalDtype`` after unpickling (:issue:`37631`)
 - Fixed regression in :meth:`DataFrame.groupby` aggregation with out-of-bounds datetime objects in an object-dtype column (:issue:`36003`)
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index ce70f929cc79d..1f6b933d643d6 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -38,6 +38,7 @@
     is_float_dtype,
     is_object_dtype,
     is_period_dtype,
+    is_sparse,
     is_string_dtype,
     is_timedelta64_dtype,
     pandas_dtype,
@@ -1956,7 +1957,11 @@ def sequence_to_dt64ns(
     data, copy = maybe_convert_dtype(data, copy)
     data_dtype = getattr(data, "dtype", None)
 
-    if is_object_dtype(data_dtype) or is_string_dtype(data_dtype):
+    if (
+        is_object_dtype(data_dtype)
+        or is_string_dtype(data_dtype)
+        or is_sparse(data_dtype)
+    ):
         # TODO: We do not have tests specific to string-dtypes,
         #  also complex or categorical or other extension
         copy = False
diff --git a/pandas/tests/indexes/datetimes/test_constructors.py b/pandas/tests/indexes/datetimes/test_constructors.py
index 3bb25adb0f36b..698da83d9e4ad 100644
--- a/pandas/tests/indexes/datetimes/test_constructors.py
+++ b/pandas/tests/indexes/datetimes/test_constructors.py
@@ -99,6 +99,17 @@ def test_dti_with_timedelta64_data_raises(self):
         with pytest.raises(TypeError, match=msg):
             to_datetime(pd.TimedeltaIndex(data))
 
+    def test_constructor_from_sparse_array(self):
+        # https://github.com/pandas-dev/pandas/issues/35843
+        values = [
+            Timestamp("2012-05-01T01:00:00.000000"),
+            Timestamp("2016-05-01T01:00:00.000000"),
+        ]
+        arr = pd.arrays.SparseArray(values)
+        result = Index(arr)
+        expected = DatetimeIndex(values)
+        tm.assert_index_equal(result, expected)
+
     def test_construction_caching(self):
 
         df = pd.DataFrame(