diff --git a/doc/source/whatsnew/v0.23.0.txt b/doc/source/whatsnew/v0.23.0.txt
index 3f300deddebeb..1273433730162 100644
--- a/doc/source/whatsnew/v0.23.0.txt
+++ b/doc/source/whatsnew/v0.23.0.txt
@@ -350,7 +350,7 @@ Reshaping
 Numeric
 ^^^^^^^
 
--
+- Bug in :func:`Series.__sub__` subtracting a non-nanosecond ``np.datetime64`` object from a ``Series`` gave incorrect results (:issue:`7996`)
 -
 -
 
diff --git a/pandas/core/ops.py b/pandas/core/ops.py
index ac9ca03c13973..05ec7f41b0c66 100644
--- a/pandas/core/ops.py
+++ b/pandas/core/ops.py
@@ -28,7 +28,7 @@
     is_datetimelike_v_numeric,
     is_integer_dtype, is_categorical_dtype,
     is_object_dtype, is_timedelta64_dtype,
-    is_datetime64_dtype, is_datetime64tz_dtype,
+    is_datetime64_dtype, is_datetime64tz_dtype, is_datetime64_ns_dtype,
     is_bool_dtype, is_datetimetz,
     is_list_like, is_offsetlike,
     is_scalar,
@@ -527,6 +527,11 @@ def _convert_to_array(self, values, name=None, other=None):
             elif not (isinstance(values, (np.ndarray, ABCSeries)) and
                       is_datetime64_dtype(values)):
                 values = libts.array_to_datetime(values)
+            elif (is_datetime64_dtype(values) and
+                  not is_datetime64_ns_dtype(values)):
+                # GH#7996 e.g. np.datetime64('2013-01-01') is datetime64[D]
+                values = values.astype('datetime64[ns]')
+
         elif inferred_type in ('timedelta', 'timedelta64'):
             # have a timedelta, convert to to ns here
             values = to_timedelta(values, errors='coerce', box=False)
diff --git a/pandas/tests/series/test_operators.py b/pandas/tests/series/test_operators.py
index 4adbdbca82fd2..433e3cf440cbd 100644
--- a/pandas/tests/series/test_operators.py
+++ b/pandas/tests/series/test_operators.py
@@ -1004,6 +1004,33 @@ def test_operators_timedelta64_with_timedelta_invalid(self, scalar_td):
 
 
 class TestDatetimeSeriesArithmetic(object):
+    @pytest.mark.parametrize(
+        'box, assert_func',
+        [(Series, tm.assert_series_equal),
+         (pd.Index, tm.assert_index_equal)])
+    def test_sub_datetime64_not_ns(self, box, assert_func):
+        # GH#7996
+        dt64 = np.datetime64('2013-01-01')
+        assert dt64.dtype == 'datetime64[D]'
+
+        obj = box(date_range('20130101', periods=3))
+        res = obj - dt64
+        expected = box([Timedelta(days=0), Timedelta(days=1),
+                        Timedelta(days=2)])
+        assert_func(res, expected)
+
+        res = dt64 - obj
+        assert_func(res, -expected)
+
+    @pytest.mark.xfail(reason='GH#7996 datetime64 units not converted to nano')
+    def test_frame_sub_datetime64_not_ns(self):
+        df = pd.DataFrame(date_range('20130101', periods=3))
+        dt64 = np.datetime64('2013-01-01')
+        assert dt64.dtype == 'datetime64[D]'
+        res = df - dt64
+        expected = pd.DataFrame([Timedelta(days=0), Timedelta(days=1),
+                                 Timedelta(days=2)])
+        tm.assert_frame_equal(res, expected)
 
     def test_operators_datetimelike(self):
         def run_ops(ops, get_ser, test_ser):