diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index f9117253b61c1..d6d33ed873564 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -130,7 +130,6 @@ Bug fixes
 ~~~~~~~~~
 - Fixed bug in :meth:`DataFrame.join` inconsistently setting result index name (:issue:`55815`)
 - Fixed bug in :meth:`Series.diff` allowing non-integer values for the ``periods`` argument. (:issue:`56607`)
--
 
 Categorical
 ^^^^^^^^^^^
@@ -219,7 +218,7 @@ Sparse
 
 ExtensionArray
 ^^^^^^^^^^^^^^
--
+- Fixed bug in :meth:`api.types.is_datetime64_any_dtype` where a custom :class:`ExtensionDtype` would return ``False`` for array-likes (:issue:`57055`)
 -
 
 Styler
diff --git a/pandas/core/dtypes/common.py b/pandas/core/dtypes/common.py
index 5e5b7bdad74d8..a53bbe9935684 100644
--- a/pandas/core/dtypes/common.py
+++ b/pandas/core/dtypes/common.py
@@ -890,7 +890,11 @@ def is_datetime64_any_dtype(arr_or_dtype) -> bool:
         tipo = _get_dtype(arr_or_dtype)
     except TypeError:
         return False
-    return lib.is_np_dtype(tipo, "M") or isinstance(tipo, DatetimeTZDtype)
+    return (
+        lib.is_np_dtype(tipo, "M")
+        or isinstance(tipo, DatetimeTZDtype)
+        or (isinstance(tipo, ExtensionDtype) and tipo.kind == "M")
+    )
 
 
 def is_datetime64_ns_dtype(arr_or_dtype) -> bool:
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index 6970c589dd36f..62e4629ca7cb7 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -53,6 +53,7 @@
 from pandas.api.extensions import no_default
 from pandas.api.types import (
     is_bool_dtype,
+    is_datetime64_any_dtype,
     is_float_dtype,
     is_integer_dtype,
     is_numeric_dtype,
@@ -1531,6 +1532,14 @@ def test_is_unsigned_integer_dtype(data):
         assert not is_unsigned_integer_dtype(data)
 
 
+def test_is_datetime64_any_dtype(data):
+    pa_type = data.dtype.pyarrow_dtype
+    if pa.types.is_timestamp(pa_type) or pa.types.is_date(pa_type):
+        assert is_datetime64_any_dtype(data)
+    else:
+        assert not is_datetime64_any_dtype(data)
+
+
 def test_is_float_dtype(data):
     pa_type = data.dtype.pyarrow_dtype
     if pa.types.is_floating(pa_type):