diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index e8b490edf8080..f1167a715afeb 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -302,6 +302,7 @@ Deprecations
 - Deprecated strings ``T``, ``t``, ``L`` and ``l`` denoting units in :func:`to_timedelta` (:issue:`52536`)
 - Deprecated the "method" and "limit" keywords on :meth:`Series.fillna`, :meth:`DataFrame.fillna`, :meth:`SeriesGroupBy.fillna`, :meth:`DataFrameGroupBy.fillna`, and :meth:`Resampler.fillna`, use ``obj.bfill()`` or ``obj.ffill()`` instead (:issue:`53394`)
 - Deprecated the ``method`` and ``limit`` keywords in :meth:`DataFrame.replace` and :meth:`Series.replace` (:issue:`33302`)
+- Deprecated the use of non-supported datetime64 and timedelta64 resolutions with :func:`pandas.array`. Supported resolutions are: "s", "ms", "us", "ns" resolutions (:issue:`53439`)
 - Deprecated values "pad", "ffill", "bfill", "backfill" for :meth:`Series.interpolate` and :meth:`DataFrame.interpolate`, use ``obj.ffill()`` or ``obj.bfill()`` instead (:issue:`53581`)
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/core/construction.py b/pandas/core/construction.py
index 9b4d67a20a7cd..76f18f55b4f1e 100644
--- a/pandas/core/construction.py
+++ b/pandas/core/construction.py
@@ -14,6 +14,7 @@
     cast,
     overload,
 )
+import warnings
 
 import numpy as np
 from numpy import ma
@@ -31,6 +32,7 @@
     DtypeObj,
     T,
 )
+from pandas.util._exceptions import find_stack_level
 
 from pandas.core.dtypes.base import ExtensionDtype
 from pandas.core.dtypes.cast import (
@@ -185,9 +187,8 @@ def array(
     Length: 2, dtype: str32
 
     Finally, Pandas has arrays that mostly overlap with NumPy
-
-      * :class:`arrays.DatetimeArray`
-      * :class:`arrays.TimedeltaArray`
+        * :class:`arrays.DatetimeArray`
+        * :class:`arrays.TimedeltaArray`
 
     When data with a ``datetime64[ns]`` or ``timedelta64[ns]`` dtype is
     passed, pandas will always return a ``DatetimeArray`` or ``TimedeltaArray``
@@ -379,6 +380,16 @@ def array(
     ):
         return TimedeltaArray._from_sequence(data, dtype=dtype, copy=copy)
 
+    elif lib.is_np_dtype(dtype, "mM"):
+        warnings.warn(
+            r"dt/td64 dtypes with 'm' and 'h' resolutions are deprecated."
+            r"Supported resolutions are 's', 'ms','us', and 'ns'. "
+            r"In future releases, 'm' and 'h' resolutions will be cast to the closest "
+            r"supported unit.",
+            FutureWarning,
+            stacklevel=find_stack_level(),
+        )
+
     return PandasArray._from_sequence(data, dtype=dtype, copy=copy)
 
 
diff --git a/pandas/tests/arrays/test_array.py b/pandas/tests/arrays/test_array.py
index 337cdaa26a3d4..06f8e24b18825 100644
--- a/pandas/tests/arrays/test_array.py
+++ b/pandas/tests/arrays/test_array.py
@@ -1,5 +1,6 @@
 import datetime
 import decimal
+import re
 
 import numpy as np
 import pytest
@@ -28,6 +29,22 @@
 )
 
 
+def test_dt64_array():
+    # PR 53439
+    dtype_unit_lst = ["M8[h]", "M8[m]", "m8[h]", "M8[m]"]
+
+    for unit in dtype_unit_lst:
+        dtype_var = np.dtype(unit)
+        msg = (
+            r"dt/td64 dtypes with 'm' and 'h' resolutions are deprecated."
+            r"Supported resolutions are 's', 'ms','us', and 'ns'. "
+            r"In future releases, 'm' and 'h' resolutions will be cast to the "
+            r"closest supported unit."
+        )
+        with tm.assert_produces_warning(FutureWarning, match=re.escape(msg)):
+            pd.array([], dtype=dtype_var)
+
+
 @pytest.mark.parametrize(
     "data, dtype, expected",
     [