diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index f7204ceb9d412..7a23fb801a29a 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -539,6 +539,8 @@ Reshaping
 - Bug in :meth:`DataFrame.append` returning incorrect dtypes with combinations of ``ExtensionDtype`` dtypes (:issue:`39454`)
 - Bug in :meth:`DataFrame.append` returning incorrect dtypes with combinations of ``datetime64`` and ``timedelta64`` dtypes (:issue:`39574`)
 - Bug in :meth:`DataFrame.pivot_table` returning a ``MultiIndex`` for a single value when operating on and empty ``DataFrame`` (:issue:`13483`)
+- Allow :class:`Index` to be passed to the :func:`numpy.all` function (:issue:`40180`)
+-
 
 Sparse
 ^^^^^^
diff --git a/pandas/compat/numpy/function.py b/pandas/compat/numpy/function.py
index 8934a02a8f5bc..3f56ecd640774 100644
--- a/pandas/compat/numpy/function.py
+++ b/pandas/compat/numpy/function.py
@@ -212,6 +212,7 @@ def validate_cum_func_with_skipna(skipna, args, kwargs, name):
 ALLANY_DEFAULTS["dtype"] = None
 ALLANY_DEFAULTS["out"] = None
 ALLANY_DEFAULTS["keepdims"] = False
+ALLANY_DEFAULTS["axis"] = None
 validate_all = CompatValidator(
     ALLANY_DEFAULTS, fname="all", method="both", max_fname_arg_count=1
 )
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 44c9b33ae51c7..7f5e7e3a32f14 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -5964,9 +5964,9 @@ def any(self, *args, **kwargs):
         Parameters
         ----------
         *args
-            These parameters will be passed to numpy.any.
+            Required for compatibility with numpy.
         **kwargs
-            These parameters will be passed to numpy.any.
+            Required for compatibility with numpy.
 
         Returns
         -------
@@ -5993,20 +5993,20 @@ def any(self, *args, **kwargs):
         >>> index.any()
         False
         """
-        # FIXME: docstr inaccurate, args/kwargs not passed
+        nv.validate_any(args, kwargs)
         self._maybe_disable_logical_methods("any")
         return np.any(self.values)
 
-    def all(self):
+    def all(self, *args, **kwargs):
         """
         Return whether all elements are Truthy.
 
         Parameters
         ----------
         *args
-            These parameters will be passed to numpy.all.
+            Required for compatibility with numpy.
         **kwargs
-            These parameters will be passed to numpy.all.
+            Required for compatibility with numpy.
 
         Returns
         -------
@@ -6050,8 +6050,7 @@ def all(self):
         >>> pd.Index([0, 0, 0]).any()
         False
         """
-        # FIXME: docstr inaccurate, args/kwargs not passed
-
+        nv.validate_all(args, kwargs)
         self._maybe_disable_logical_methods("all")
         return np.all(self.values)
 
diff --git a/pandas/tests/reductions/test_reductions.py b/pandas/tests/reductions/test_reductions.py
index e3145e0cc5c9f..77b549e675a8d 100644
--- a/pandas/tests/reductions/test_reductions.py
+++ b/pandas/tests/reductions/test_reductions.py
@@ -898,6 +898,15 @@ def test_all_any(self):
         s = Series(["abc", True])
         assert "abc" == s.any()  # 'abc' || True => 'abc'
 
+    @pytest.mark.parametrize("klass", [Index, Series])
+    def test_numpy_all_any(self, klass):
+        # GH#40180
+        idx = klass([0, 1, 2])
+        assert not np.all(idx)
+        assert np.any(idx)
+        idx = Index([1, 2, 3])
+        assert np.all(idx)
+
     def test_all_any_params(self):
         # Check skipna, with implicit 'object' dtype.
         s1 = Series([np.nan, True])