diff --git a/pandas/core/dtypes/dtypes.py b/pandas/core/dtypes/dtypes.py
index 8fe2b3c60d6d0..be43e3a6c856b 100644
--- a/pandas/core/dtypes/dtypes.py
+++ b/pandas/core/dtypes/dtypes.py
@@ -798,6 +798,8 @@ def __hash__(self) -> int:
 
     def __eq__(self, other: Any) -> bool:
         if isinstance(other, str):
+            if other.startswith("M8["):
+                other = "datetime64[" + other[3:]
             return other == self.name
 
         return (
diff --git a/pandas/tests/dtypes/test_common.py b/pandas/tests/dtypes/test_common.py
index b9c8f3a8dd494..1708139a397ab 100644
--- a/pandas/tests/dtypes/test_common.py
+++ b/pandas/tests/dtypes/test_common.py
@@ -75,6 +75,10 @@ def test_numpy_string_dtype(self):
             "datetime64[ns, US/Eastern]",
             "datetime64[ns, Asia/Tokyo]",
             "datetime64[ns, UTC]",
+            # GH#33885 check that the M8 alias is understood
+            "M8[ns, US/Eastern]",
+            "M8[ns, Asia/Tokyo]",
+            "M8[ns, UTC]",
         ],
     )
     def test_datetimetz_dtype(self, dtype):
diff --git a/pandas/tests/dtypes/test_dtypes.py b/pandas/tests/dtypes/test_dtypes.py
index 519f2f3eead1c..b55ff92e3f6a4 100644
--- a/pandas/tests/dtypes/test_dtypes.py
+++ b/pandas/tests/dtypes/test_dtypes.py
@@ -278,12 +278,14 @@ def test_is_dtype(self, dtype):
         assert not DatetimeTZDtype.is_dtype(None)
         assert DatetimeTZDtype.is_dtype(dtype)
         assert DatetimeTZDtype.is_dtype("datetime64[ns, US/Eastern]")
+        assert DatetimeTZDtype.is_dtype("M8[ns, US/Eastern]")
         assert not DatetimeTZDtype.is_dtype("foo")
         assert DatetimeTZDtype.is_dtype(DatetimeTZDtype("ns", "US/Pacific"))
         assert not DatetimeTZDtype.is_dtype(np.float64)
 
     def test_equality(self, dtype):
         assert is_dtype_equal(dtype, "datetime64[ns, US/Eastern]")
+        assert is_dtype_equal(dtype, "M8[ns, US/Eastern]")
         assert is_dtype_equal(dtype, DatetimeTZDtype("ns", "US/Eastern"))
         assert not is_dtype_equal(dtype, "foo")
         assert not is_dtype_equal(dtype, DatetimeTZDtype("ns", "CET"))
@@ -294,6 +296,8 @@ def test_equality(self, dtype):
         # numpy compat
         assert is_dtype_equal(np.dtype("M8[ns]"), "datetime64[ns]")
 
+        assert dtype == "M8[ns, US/Eastern]"
+
     def test_basic(self, dtype):
 
         assert is_datetime64tz_dtype(dtype)