diff --git a/pandas/compat/numpy/function.py b/pandas/compat/numpy/function.py
index d42be56963569..a4232ca2ebf78 100644
--- a/pandas/compat/numpy/function.py
+++ b/pandas/compat/numpy/function.py
@@ -360,3 +360,24 @@ def validate_resampler_func(method, args, kwargs):
                 "{func}() instead".format(func=method)))
         else:
             raise TypeError("too many arguments passed in")
+
+
+def validate_minmax_axis(axis):
+    """
+    Ensure that the axis argument passed to min, max, argmin, or argmax is
+    zero or None, as otherwise it will be incorrectly ignored.
+
+    Parameters
+    ----------
+    axis : int or None
+
+    Raises
+    ------
+    ValueError
+    """
+    ndim = 1  # hard-coded for Index
+    if axis is None:
+        return
+    if axis >= ndim or (axis < 0 and ndim + axis < 0):
+        raise ValueError("`axis` must be fewer than the number of "
+                         "dimensions ({ndim})".format(ndim=ndim))
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 8e919ba3599fc..d9152c50309eb 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -431,6 +431,7 @@ def min(self, axis=None, *args, **kwargs):
         numpy.ndarray.min
         """
         nv.validate_min(args, kwargs)
+        nv.validate_minmax_axis(axis)
 
         try:
             i8 = self.asi8
@@ -459,6 +460,7 @@ def argmin(self, axis=None, *args, **kwargs):
         numpy.ndarray.argmin
         """
         nv.validate_argmin(args, kwargs)
+        nv.validate_minmax_axis(axis)
 
         i8 = self.asi8
         if self.hasnans:
@@ -479,6 +481,7 @@ def max(self, axis=None, *args, **kwargs):
         numpy.ndarray.max
         """
         nv.validate_max(args, kwargs)
+        nv.validate_minmax_axis(axis)
 
         try:
             i8 = self.asi8
@@ -507,6 +510,7 @@ def argmax(self, axis=None, *args, **kwargs):
         numpy.ndarray.argmax
         """
         nv.validate_argmax(args, kwargs)
+        nv.validate_minmax_axis(axis)
 
         i8 = self.asi8
         if self.hasnans:
diff --git a/pandas/tests/indexes/datetimelike.py b/pandas/tests/indexes/datetimelike.py
index e32e18ea0ec4a..7af8b259fa137 100644
--- a/pandas/tests/indexes/datetimelike.py
+++ b/pandas/tests/indexes/datetimelike.py
@@ -8,6 +8,18 @@
 
 class DatetimeLike(Base):
 
+    def test_argmax_axis_invalid(self):
+        # GH#23081
+        rng = self.create_index()
+        with pytest.raises(ValueError):
+            rng.argmax(axis=1)
+        with pytest.raises(ValueError):
+            rng.argmin(axis=2)
+        with pytest.raises(ValueError):
+            rng.min(axis=-2)
+        with pytest.raises(ValueError):
+            rng.max(axis=-3)
+
     def test_can_hold_identifiers(self):
         idx = self.create_index()
         key = idx[0]