diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 66b6923ef13e4..777cb42080f98 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -642,6 +642,7 @@ Timedelta
 - Bug in :class:`Series` with numeric dtype when adding or subtracting an an array or ``Series`` with ``timedelta64`` dtype (:issue:`22390`)
 - Bug in :class:`Index` with numeric dtype when multiplying or dividing an array with dtype ``timedelta64`` (:issue:`22390`)
 - Bug in :class:`TimedeltaIndex` incorrectly allowing indexing with ``Timestamp`` object (:issue:`20464`)
+- Fixed bug where subtracting :class:`Timedelta` from an object-dtyped array would raise ``TypeError`` (:issue:`21980`)
 -
 -
 
diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index 9b13ef5982396..9c8be1901d1dc 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -541,10 +541,12 @@ def _binary_op_method_timedeltalike(op, name):
 
         elif hasattr(other, 'dtype'):
             # nd-array like
-            if other.dtype.kind not in ['m', 'M']:
-                # raise rathering than letting numpy return wrong answer
+            if other.dtype.kind in ['m', 'M']:
+                return op(self.to_timedelta64(), other)
+            elif other.dtype.kind == 'O':
+                return np.array([op(self, x) for x in other])
+            else:
                 return NotImplemented
-            return op(self.to_timedelta64(), other)
 
         elif not _validate_ops_compat(other):
             return NotImplemented
diff --git a/pandas/tests/scalar/timedelta/test_arithmetic.py b/pandas/tests/scalar/timedelta/test_arithmetic.py
index 9636c92ec22d5..fce1ef29235cc 100644
--- a/pandas/tests/scalar/timedelta/test_arithmetic.py
+++ b/pandas/tests/scalar/timedelta/test_arithmetic.py
@@ -200,6 +200,57 @@ def test_td_rsub_numeric_raises(self):
         with pytest.raises(TypeError):
             2.0 - td
 
+    def test_td_sub_timedeltalike_object_dtype_array(self):
+        # GH 21980
+        arr = np.array([Timestamp('20130101 9:01'),
+                        Timestamp('20121230 9:02')])
+        exp = np.array([Timestamp('20121231 9:01'),
+                        Timestamp('20121229 9:02')])
+        res = arr - pd.Timedelta('1D')
+        tm.assert_numpy_array_equal(res, exp)
+
+    def test_td_sub_mixed_most_timedeltalike_object_dtype_array(self):
+        # GH 21980
+        now = pd.Timestamp.now()
+        arr = np.array([now,
+                        pd.Timedelta('1D'),
+                        np.timedelta64(2, 'h')])
+        exp = np.array([now - pd.Timedelta('1D'),
+                        pd.Timedelta('0D'),
+                        np.timedelta64(2, 'h') - pd.Timedelta('1D')])
+        res = arr - pd.Timedelta('1D')
+        tm.assert_numpy_array_equal(res, exp)
+
+    def test_td_rsub_mixed_most_timedeltalike_object_dtype_array(self):
+        # GH 21980
+        now = pd.Timestamp.now()
+        arr = np.array([now,
+                        pd.Timedelta('1D'),
+                        np.timedelta64(2, 'h')])
+        with pytest.raises(TypeError):
+            pd.Timedelta('1D') - arr
+
+    @pytest.mark.parametrize('op', [operator.add, ops.radd])
+    def test_td_add_timedeltalike_object_dtype_array(self, op):
+        # GH 21980
+        arr = np.array([Timestamp('20130101 9:01'),
+                        Timestamp('20121230 9:02')])
+        exp = np.array([Timestamp('20130102 9:01'),
+                        Timestamp('20121231 9:02')])
+        res = op(arr, pd.Timedelta('1D'))
+        tm.assert_numpy_array_equal(res, exp)
+
+    @pytest.mark.parametrize('op', [operator.add, ops.radd])
+    def test_td_add_mixed_timedeltalike_object_dtype_array(self, op):
+        # GH 21980
+        now = pd.Timestamp.now()
+        arr = np.array([now,
+                        pd.Timedelta('1D')])
+        exp = np.array([now + pd.Timedelta('1D'),
+                        pd.Timedelta('2D')])
+        res = op(arr, pd.Timedelta('1D'))
+        tm.assert_numpy_array_equal(res, exp)
+
 
 class TestTimedeltaMultiplicationDivision(object):
     """
@@ -616,3 +667,17 @@ def test_rdivmod_invalid(self):
 
         with pytest.raises(TypeError):
             divmod(np.array([22, 24]), td)
+
+    @pytest.mark.parametrize('op', [
+        operator.mul,
+        ops.rmul,
+        operator.truediv,
+        ops.rdiv,
+        ops.rsub])
+    @pytest.mark.parametrize('arr', [
+        np.array([Timestamp('20130101 9:01'), Timestamp('20121230 9:02')]),
+        np.array([pd.Timestamp.now(), pd.Timedelta('1D')])
+    ])
+    def test_td_op_timedelta_timedeltalike_array(self, op, arr):
+        with pytest.raises(TypeError):
+            op(arr, pd.Timedelta('1D'))