diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 64b9a11b1980d..7c4db6865135a 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -180,7 +180,7 @@ Datetimelike
 ^^^^^^^^^^^^
 - Bug in :class:`DataFrame` and :class:`Series` constructors sometimes dropping nanoseconds from :class:`Timestamp` (resp. :class:`Timedelta`) ``data``, with ``dtype=datetime64[ns]`` (resp. ``timedelta64[ns]``) (:issue:`38032`)
 - Bug in :meth:`DataFrame.first` and :meth:`Series.first` returning two months for offset one month when first day is last calendar day (:issue:`29623`)
--
+- Bug in constructing a :class:`DataFrame` or :class:`Series` with mismatched ``datetime64`` data and ``timedelta64`` dtype, or vice-versa, failing to raise ``TypeError`` (:issue:`38575`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index d1c16de05ce55..80a1617e0b735 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -164,6 +164,14 @@ def maybe_unbox_datetimelike(value: Scalar, dtype: DtypeObj) -> Scalar:
             value = value.to_datetime64()
     elif isinstance(value, Timedelta):
         value = value.to_timedelta64()
+
+    if (isinstance(value, np.timedelta64) and dtype.kind == "M") or (
+        isinstance(value, np.datetime64) and dtype.kind == "m"
+    ):
+        # numpy allows np.array(dt64values, dtype="timedelta64[ns]") and
+        #  vice-versa, but we do not want to allow this, so we need to
+        #  check explicitly
+        raise TypeError(f"Cannot cast {repr(value)} to {dtype}")
     return value
 
 
diff --git a/pandas/tests/dtypes/cast/test_construct_from_scalar.py b/pandas/tests/dtypes/cast/test_construct_from_scalar.py
index a6f97563311a7..4ff3375d1988d 100644
--- a/pandas/tests/dtypes/cast/test_construct_from_scalar.py
+++ b/pandas/tests/dtypes/cast/test_construct_from_scalar.py
@@ -1,4 +1,5 @@
 import numpy as np
+import pytest
 
 from pandas.core.dtypes.cast import construct_1d_arraylike_from_scalar
 from pandas.core.dtypes.dtypes import CategoricalDtype
@@ -32,3 +33,20 @@ def test_cast_1d_array_like_from_timedelta():
     td = Timedelta(1)
     res = construct_1d_arraylike_from_scalar(td, 2, np.dtype("m8[ns]"))
     assert res[0] == td
+
+
+def test_cast_1d_array_like_mismatched_datetimelike():
+    td = np.timedelta64("NaT", "ns")
+    dt = np.datetime64("NaT", "ns")
+
+    with pytest.raises(TypeError, match="Cannot cast"):
+        construct_1d_arraylike_from_scalar(td, 2, dt.dtype)
+
+    with pytest.raises(TypeError, match="Cannot cast"):
+        construct_1d_arraylike_from_scalar(np.timedelta64(4, "ns"), 2, dt.dtype)
+
+    with pytest.raises(TypeError, match="Cannot cast"):
+        construct_1d_arraylike_from_scalar(dt, 2, td.dtype)
+
+    with pytest.raises(TypeError, match="Cannot cast"):
+        construct_1d_arraylike_from_scalar(np.datetime64(4, "ns"), 2, td.dtype)
diff --git a/pandas/tests/frame/test_constructors.py b/pandas/tests/frame/test_constructors.py
index 3d4fbc74d0e6a..5ba38016ee552 100644
--- a/pandas/tests/frame/test_constructors.py
+++ b/pandas/tests/frame/test_constructors.py
@@ -2962,3 +2962,15 @@ def test_from_timedelta64_scalar_object(self, constructor, request):
 
         obj = constructor(td64, dtype=object)
         assert isinstance(get1(obj), np.timedelta64)
+
+    @pytest.mark.parametrize("cls", [np.datetime64, np.timedelta64])
+    def test_from_scalar_datetimelike_mismatched(self, constructor, cls):
+        scalar = cls("NaT", "ns")
+        dtype = {np.datetime64: "m8[ns]", np.timedelta64: "M8[ns]"}[cls]
+
+        with pytest.raises(TypeError, match="Cannot cast"):
+            constructor(scalar, dtype=dtype)
+
+        scalar = cls(4, "ns")
+        with pytest.raises(TypeError, match="Cannot cast"):
+            constructor(scalar, dtype=dtype)