diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 5b09b62fa9e88..ae00309ba964d 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -150,6 +150,7 @@ Deprecations
 - Deprecated :meth:`Index.is_type_compatible` (:issue:`42113`)
 - Deprecated ``method`` argument in :meth:`Index.get_loc`, use ``index.get_indexer([label], method=...)`` instead (:issue:`42269`)
 - Deprecated treating integer keys in :meth:`Series.__setitem__` as positional when the index is a :class:`Float64Index` not containing the key, a :class:`IntervalIndex` with no entries containing the key, or a :class:`MultiIndex` with leading :class:`Float64Index` level not containing the key (:issue:`33469`)
+- Deprecated treating ``numpy.datetime64`` objects as UTC times when passed to the :class:`Timestamp` constructor along with a timezone. In a future version, these will be treated as wall-times. To retain the old behavior, use ``Timestamp(dt64).tz_localize("UTC").tz_convert(tz)`` (:issue:`24559`)
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index 88a2706a35aa2..e4e9df5176459 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -1329,6 +1329,19 @@ class Timestamp(_Timestamp):
                              "the tz parameter. Use tz_convert instead.")
 
         tzobj = maybe_get_tz(tz)
+        if tzobj is not None and is_datetime64_object(ts_input):
+            # GH#24559, GH#42288 In the future we will treat datetime64 as
+            #  wall-time (consistent with DatetimeIndex)
+            warnings.warn(
+                "In a future version, when passing a np.datetime64 object and "
+                "a timezone to Timestamp, the datetime64 will be interpreted "
+                "as a wall time, not a UTC time.  To interpret as a UTC time, "
+                "use `Timestamp(dt64).tz_localize('UTC').tz_convert(tz)`",
+                FutureWarning,
+                stacklevel=1,
+            )
+            # Once this deprecation is enforced, we can do
+            #  return Timestamp(ts_input).tz_localize(tzobj)
         ts = convert_to_tsobject(ts_input, tzobj, unit, 0, 0, nanosecond or 0)
 
         if ts.value == NPY_NAT:
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index 0a517b22d1bb3..8513bbb044e83 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -509,6 +509,11 @@ def _check_compatible_with(self, other, setitem: bool = False):
     # Descriptive Properties
 
     def _box_func(self, x) -> Timestamp | NaTType:
+        if isinstance(x, np.datetime64):
+            # GH#42228
+            # Argument 1 to "signedinteger" has incompatible type "datetime64";
+            # expected "Union[SupportsInt, Union[str, bytes], SupportsIndex]"
+            x = np.int64(x)  # type: ignore[arg-type]
         ts = Timestamp(x, tz=self.tz)
         # Non-overlapping identity check (left operand type: "Timestamp",
         # right operand type: "NaTType")
diff --git a/pandas/tests/scalar/timestamp/test_constructors.py b/pandas/tests/scalar/timestamp/test_constructors.py
index c6c475f5b87a2..b3deb1a57e5c3 100644
--- a/pandas/tests/scalar/timestamp/test_constructors.py
+++ b/pandas/tests/scalar/timestamp/test_constructors.py
@@ -24,6 +24,24 @@
 
 
 class TestTimestampConstructors:
+    def test_constructor_datetime64_with_tz(self):
+        # GH#42288, GH#24559
+        dt = np.datetime64("1970-01-01 05:00:00")
+        tzstr = "UTC+05:00"
+
+        msg = "interpreted as a wall time"
+        with tm.assert_produces_warning(FutureWarning, match=msg):
+            ts = Timestamp(dt, tz=tzstr)
+
+        # Check that we match the old behavior
+        alt = Timestamp(dt).tz_localize("UTC").tz_convert(tzstr)
+        assert ts == alt
+
+        # Check that we *don't* match the future behavior
+        assert ts.hour != 5
+        expected_future = Timestamp(dt).tz_localize(tzstr)
+        assert ts != expected_future
+
     def test_constructor(self):
         base_str = "2014-07-01 09:00"
         base_dt = datetime(2014, 7, 1, 9)