diff --git a/doc/source/whatsnew/v1.1.2.rst b/doc/source/whatsnew/v1.1.2.rst
index c1b73c60be92b..c9ead81c6d780 100644
--- a/doc/source/whatsnew/v1.1.2.rst
+++ b/doc/source/whatsnew/v1.1.2.rst
@@ -25,6 +25,7 @@ Fixed regressions
 Bug fixes
 ~~~~~~~~~
 - Bug in :meth:`DataFrame.eval` with ``object`` dtype column binary operations (:issue:`35794`)
+- Bug in :class:`Series` constructor raising a ``TypeError`` when constructing sparse datetime64 dtypes (:issue:`35762`)
 - Bug in :meth:`DataFrame.apply` with ``result_type="reduce"`` returning with incorrect index (:issue:`35683`)
 -
 -
diff --git a/pandas/core/construction.py b/pandas/core/construction.py
index 47f10f1f65f4a..e8c9f28e50084 100644
--- a/pandas/core/construction.py
+++ b/pandas/core/construction.py
@@ -35,6 +35,7 @@
     is_iterator,
     is_list_like,
     is_object_dtype,
+    is_sparse,
     is_timedelta64_ns_dtype,
 )
 from pandas.core.dtypes.generic import (
@@ -535,9 +536,10 @@ def _try_cast(
         if maybe_castable(arr) and not copy and dtype is None:
             return arr
 
-    if isinstance(dtype, ExtensionDtype) and dtype.kind != "M":
+    if isinstance(dtype, ExtensionDtype) and (dtype.kind != "M" or is_sparse(dtype)):
         # create an extension array from its dtype
-        # DatetimeTZ case needs to go through maybe_cast_to_datetime
+        # DatetimeTZ case needs to go through maybe_cast_to_datetime but
+        # SparseDtype does not
         array_type = dtype.construct_array_type()._from_sequence
         subarr = array_type(arr, dtype=dtype, copy=copy)
         return subarr
diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index 2697f42eb05a4..e6b4cb598989b 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -50,6 +50,7 @@
     is_numeric_dtype,
     is_object_dtype,
     is_scalar,
+    is_sparse,
     is_string_dtype,
     is_timedelta64_dtype,
     is_timedelta64_ns_dtype,
@@ -1323,7 +1324,9 @@ def maybe_cast_to_datetime(value, dtype, errors: str = "raise"):
                 f"Please pass in '{dtype.name}[ns]' instead."
             )
 
-            if is_datetime64 and not is_dtype_equal(dtype, DT64NS_DTYPE):
+            if is_datetime64 and not is_dtype_equal(
+                getattr(dtype, "subtype", dtype), DT64NS_DTYPE
+            ):
 
                 # pandas supports dtype whose granularity is less than [ns]
                 # e.g., [ps], [fs], [as]
@@ -1355,7 +1358,7 @@ def maybe_cast_to_datetime(value, dtype, errors: str = "raise"):
             if is_scalar(value):
                 if value == iNaT or isna(value):
                     value = iNaT
-            else:
+            elif not is_sparse(value):
                 value = np.array(value, copy=False)
 
                 # have a scalar array-like (e.g. NaT)
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index 1dd410ad02ee0..bcf7039ec9039 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -1449,3 +1449,18 @@ def test_constructor_datetimelike_scalar_to_string_dtype(self):
         result = Series("M", index=[1, 2, 3], dtype="string")
         expected = pd.Series(["M", "M", "M"], index=[1, 2, 3], dtype="string")
         tm.assert_series_equal(result, expected)
+
+    @pytest.mark.parametrize(
+        "values",
+        [
+            [np.datetime64("2012-01-01"), np.datetime64("2013-01-01")],
+            ["2012-01-01", "2013-01-01"],
+        ],
+    )
+    def test_constructor_sparse_datetime64(self, values):
+        # https://github.com/pandas-dev/pandas/issues/35762
+        dtype = pd.SparseDtype("datetime64[ns]")
+        result = pd.Series(values, dtype=dtype)
+        arr = pd.arrays.SparseArray(values, dtype=dtype)
+        expected = pd.Series(arr)
+        tm.assert_series_equal(result, expected)