diff --git a/doc/source/whatsnew/v1.1.3.rst b/doc/source/whatsnew/v1.1.3.rst
index 3f8413bd492ca..1d386fa372ce1 100644
--- a/doc/source/whatsnew/v1.1.3.rst
+++ b/doc/source/whatsnew/v1.1.3.rst
@@ -34,7 +34,7 @@ Fixed regressions
 - Fixed regression in :meth:`Series.__getitem__` incorrectly raising when the input was a tuple (:issue:`35534`)
 - Fixed regression in :meth:`Series.__getitem__` incorrectly raising when the input was a frozenset (:issue:`35747`)
 - Fixed regression in :meth:`read_excel` with ``engine="odf"`` caused ``UnboundLocalError`` in some cases where cells had nested child nodes (:issue:`36122`,:issue:`35802`)
--
+- Fixed regression in :class:`DataFrame` and :class:`Series` comparisons between numeric arrays and strings (:issue:`35700`,:issue:`36377`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 222ae589ea7fc..5ca51ca496b80 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -138,10 +138,14 @@ def cmp_method(self, other):
             with np.errstate(all="ignore"):
                 result = ops.comp_method_OBJECT_ARRAY(op, self._values, other)
 
-        else:
+        elif is_interval_dtype(self.dtype):
             with np.errstate(all="ignore"):
                 result = op(self._values, np.asarray(other))
 
+        else:
+            with np.errstate(all="ignore"):
+                result = ops.comparison_op(self._values, np.asarray(other), op)
+
         if is_bool_dtype(result):
             return result
         return ops.invalid_comparison(self, other, op)
diff --git a/pandas/core/ops/array_ops.py b/pandas/core/ops/array_ops.py
index aab10cea33632..fd5f126051c53 100644
--- a/pandas/core/ops/array_ops.py
+++ b/pandas/core/ops/array_ops.py
@@ -23,6 +23,7 @@
     is_bool_dtype,
     is_integer_dtype,
     is_list_like,
+    is_numeric_v_string_like,
     is_object_dtype,
     is_scalar,
 )
@@ -235,6 +236,10 @@ def comparison_op(left: ArrayLike, right: Any, op) -> ArrayLike:
         else:
             res_values = np.zeros(lvalues.shape, dtype=bool)
 
+    elif is_numeric_v_string_like(lvalues, rvalues):
+        # GH#36377 going through the numexpr path would incorrectly raise
+        return invalid_comparison(lvalues, rvalues, op)
+
     elif is_object_dtype(lvalues.dtype):
         res_values = comp_method_OBJECT_ARRAY(op, lvalues, rvalues)
 
diff --git a/pandas/tests/arithmetic/test_numeric.py b/pandas/tests/arithmetic/test_numeric.py
index ecac08ffe3ba2..139401bdf5806 100644
--- a/pandas/tests/arithmetic/test_numeric.py
+++ b/pandas/tests/arithmetic/test_numeric.py
@@ -89,6 +89,26 @@ def test_compare_invalid(self):
         b.name = pd.Timestamp("2000-01-01")
         tm.assert_series_equal(a / b, 1 / (b / a))
 
+    def test_numeric_cmp_string_numexpr_path(self, box):
+        # GH#36377, GH#35700
+        xbox = box if box is not pd.Index else np.ndarray
+
+        obj = pd.Series(np.random.randn(10 ** 5))
+        obj = tm.box_expected(obj, box, transpose=False)
+
+        result = obj == "a"
+
+        expected = pd.Series(np.zeros(10 ** 5, dtype=bool))
+        expected = tm.box_expected(expected, xbox, transpose=False)
+        tm.assert_equal(result, expected)
+
+        result = obj != "a"
+        tm.assert_equal(result, ~expected)
+
+        msg = "Invalid comparison between dtype=float64 and str"
+        with pytest.raises(TypeError, match=msg):
+            obj < "a"
+
 
 # ------------------------------------------------------------------
 # Numeric dtypes Arithmetic with Datetime/Timedelta Scalar
diff --git a/pandas/tests/indexes/test_numpy_compat.py b/pandas/tests/indexes/test_numpy_compat.py
index a83684464caf6..b71417b2a625d 100644
--- a/pandas/tests/indexes/test_numpy_compat.py
+++ b/pandas/tests/indexes/test_numpy_compat.py
@@ -114,18 +114,3 @@ def test_numpy_ufuncs_other(index, func):
         else:
             with pytest.raises(Exception):
                 func(index)
-
-
-def test_elementwise_comparison_warning():
-    # https://github.com/pandas-dev/pandas/issues/22698#issuecomment-458968300
-    # np.array([1, 2]) == 'a' returns False, and produces a
-    # FutureWarning that it'll be [False, False] in the future.
-    # We just want to ensure that comes through.
-    # When NumPy dev actually enforces this change, we'll need to skip
-    # this test.
-    idx = Index([1, 2])
-    with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-        result = idx == "a"
-
-    expected = np.array([False, False])
-    tm.assert_numpy_array_equal(result, expected)