diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index cca6238d2e89ac..ba164a82c162e8 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -942,7 +942,7 @@ Removal of prior version deprecations/changes
 - Removal of the previously deprecated module ``pandas.core.datetools`` (:issue:`14105`, :issue:`14094`)
 - Strings passed into :meth:`DataFrame.groupby` that refer to both column and index levels will raise a ``ValueError`` (:issue:`14432`)
 - :meth:`Index.repeat` and :meth:`MultiIndex.repeat` have renamed the ``n`` argument to ``repeats`` (:issue:`14645`)
-- The ``Series`` constructor and ``.astype`` method will now raise a ``ValueError`` if timestamp dtypes are passed in without a frequency (e.g. ``np.datetime64``) for the ``dtype`` parameter (:issue:`15987`)
+- The ``Series`` constructor and ``.astype`` method will now raise a ``ValueError`` if timestamp dtypes are passed in without a unit (e.g. ``np.datetime64``) for the ``dtype`` parameter (:issue:`15987`)
 - Removal of the previously deprecated ``as_indexer`` keyword completely from ``str.match()`` (:issue:`22356`, :issue:`6581`)
 - The modules ``pandas.types``, ``pandas.computation``, and ``pandas.util.decorators`` have been removed (:issue:`16157`, :issue:`16250`)
 - Removed the ``pandas.formats.style`` shim for :class:`pandas.io.formats.style.Styler` (:issue:`16059`)
diff --git a/doc/test.parquet b/doc/test.parquet
new file mode 100644
index 00000000000000..cc2f7edbb6ee4b
Binary files /dev/null and b/doc/test.parquet differ
diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index f8b7fb7d88ee00..47e17c9868cd78 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -667,7 +667,7 @@ def astype_nansafe(arr, dtype, copy=True, skipna=False):
     Raises
     ------
     ValueError
-        The dtype was a datetime /timedelta dtype, but it had no frequency.
+        The dtype was a datetime64/timedelta64 dtype, but it had no unit.
     """
 
     # dispatch on extension dtype if needed
@@ -749,7 +749,7 @@ def astype_nansafe(arr, dtype, copy=True, skipna=False):
             return astype_nansafe(to_timedelta(arr).values, dtype, copy=copy)
 
     if dtype.name in ("datetime64", "timedelta64"):
-        msg = ("The '{dtype}' dtype has no frequency. "
+        msg = ("The '{dtype}' dtype has no unit. "
                "Please pass in '{dtype}[ns]' instead.")
         raise ValueError(msg.format(dtype=dtype.name))
 
@@ -1021,7 +1021,7 @@ def maybe_cast_to_datetime(value, dtype, errors='raise'):
         if is_datetime64 or is_datetime64tz or is_timedelta64:
 
             # Force the dtype if needed.
-            msg = ("The '{dtype}' dtype has no frequency. "
+            msg = ("The '{dtype}' dtype has no unit. "
                    "Please pass in '{dtype}[ns]' instead.")
 
             if is_datetime64 and not is_dtype_equal(dtype, _NS_DTYPE):
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index bdd99dd4850422..7595b1278a2916 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -1198,7 +1198,7 @@ def test_constructor_cast_object(self, index):
     ])
     def test_constructor_generic_timestamp_no_frequency(self, dtype):
         # see gh-15524, gh-15987
-        msg = "dtype has no frequency. Please pass in"
+        msg = "dtype has no unit. Please pass in"
 
         with tm.assert_raises_regex(ValueError, msg):
             Series([], dtype=dtype)
diff --git a/pandas/tests/series/test_dtypes.py b/pandas/tests/series/test_dtypes.py
index c62531241369d8..64184a6465ba3f 100644
--- a/pandas/tests/series/test_dtypes.py
+++ b/pandas/tests/series/test_dtypes.py
@@ -404,7 +404,7 @@ def test_astype_generic_timestamp_no_frequency(self, dtype):
         data = [1]
         s = Series(data)
 
-        msg = "dtype has no frequency. Please pass in"
+        msg = "dtype has no unit. Please pass in"
         with tm.assert_raises_regex(ValueError, msg):
             s.astype(dtype)