diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 578e24009d35a..e0b4baf5d8543 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -433,6 +433,7 @@ Other
 
 - Removed unused C functions from vendored UltraJSON implementation (:issue:`26198`)
 - Bug in :func:`factorize` when passing an ``ExtensionArray`` with a custom ``na_sentinel`` (:issue:`25696`).
+- Allow :class:`Index` and :class:`RangeIndex` to be passed to numpy ``min`` and ``max`` functions.
 
 
 .. _whatsnew_0.250.contributors:
diff --git a/pandas/core/base.py b/pandas/core/base.py
index 72db3cee0e80f..5bccaeef66a82 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -981,7 +981,7 @@ def _ndarray_values(self) -> np.ndarray:
     def empty(self):
         return not self.size
 
-    def max(self, axis=None, skipna=True):
+    def max(self, axis=None, skipna=True, *args, **kwargs):
         """
         Return the maximum value of the Index.
 
@@ -1019,9 +1019,10 @@ def max(self, axis=None, skipna=True):
         ('b', 2)
         """
         nv.validate_minmax_axis(axis)
+        nv.validate_max(args, kwargs)
         return nanops.nanmax(self._values, skipna=skipna)
 
-    def argmax(self, axis=None, skipna=True):
+    def argmax(self, axis=None, skipna=True, *args, **kwargs):
         """
         Return an ndarray of the maximum argument indexer.
 
@@ -1041,9 +1042,10 @@ def argmax(self, axis=None, skipna=True):
         numpy.ndarray.argmax
         """
         nv.validate_minmax_axis(axis)
+        nv.validate_argmax_with_skipna(skipna, args, kwargs)
         return nanops.nanargmax(self._values, skipna=skipna)
 
-    def min(self, axis=None, skipna=True):
+    def min(self, axis=None, skipna=True, *args, **kwargs):
         """
         Return the minimum value of the Index.
 
@@ -1081,9 +1083,10 @@ def min(self, axis=None, skipna=True):
         ('a', 1)
         """
         nv.validate_minmax_axis(axis)
+        nv.validate_min(args, kwargs)
         return nanops.nanmin(self._values, skipna=skipna)
 
-    def argmin(self, axis=None, skipna=True):
+    def argmin(self, axis=None, skipna=True, *args, **kwargs):
         """
         Return a ndarray of the minimum argument indexer.
 
@@ -1102,6 +1105,7 @@ def argmin(self, axis=None, skipna=True):
         numpy.ndarray.argmin
         """
         nv.validate_minmax_axis(axis)
+        nv.validate_argmax_with_skipna(skipna, args, kwargs)
         return nanops.nanargmin(self._values, skipna=skipna)
 
     def tolist(self):
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index e969c4b695d30..160e6284d3c59 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -327,14 +327,16 @@ def _minmax(self, meth):
 
         return self._start + self._step * no_steps
 
-    def min(self, axis=None, skipna=True):
+    def min(self, axis=None, skipna=True, *args, **kwargs):
         """The minimum value of the RangeIndex"""
         nv.validate_minmax_axis(axis)
+        nv.validate_min(args, kwargs)
         return self._minmax('min')
 
-    def max(self, axis=None, skipna=True):
+    def max(self, axis=None, skipna=True, *args, **kwargs):
         """The maximum value of the RangeIndex"""
         nv.validate_minmax_axis(axis)
+        nv.validate_max(args, kwargs)
         return self._minmax('max')
 
     def argsort(self, *args, **kwargs):
diff --git a/pandas/tests/reductions/test_reductions.py b/pandas/tests/reductions/test_reductions.py
index c91233e9317b7..61ab759aa8d9b 100644
--- a/pandas/tests/reductions/test_reductions.py
+++ b/pandas/tests/reductions/test_reductions.py
@@ -318,6 +318,59 @@ def test_minmax_nat_datetime64(self, op):
         obj = DatetimeIndex([pd.NaT, pd.NaT, pd.NaT])
         assert pd.isna(getattr(obj, op)())
 
+    def test_numpy_minmax_integer(self):
+        # GH#26125
+        idx = Index([1, 2, 3])
+
+        expected = idx.values.max()
+        result = np.max(idx)
+        assert result == expected
+
+        expected = idx.values.min()
+        result = np.min(idx)
+        assert result == expected
+
+        errmsg = "the 'out' parameter is not supported"
+        with pytest.raises(ValueError, match=errmsg):
+            np.min(idx, out=0)
+        with pytest.raises(ValueError, match=errmsg):
+            np.max(idx, out=0)
+
+        expected = idx.values.argmax()
+        result = np.argmax(idx)
+        assert result == expected
+
+        expected = idx.values.argmin()
+        result = np.argmin(idx)
+        assert result == expected
+
+        errmsg = "the 'out' parameter is not supported"
+        with pytest.raises(ValueError, match=errmsg):
+            np.argmin(idx, out=0)
+        with pytest.raises(ValueError, match=errmsg):
+            np.argmax(idx, out=0)
+
+    def test_numpy_minmax_range(self):
+        # GH#26125
+        idx = RangeIndex(0, 10, 3)
+
+        expected = idx._int64index.max()
+        result = np.max(idx)
+        assert result == expected
+
+        expected = idx._int64index.min()
+        result = np.min(idx)
+        assert result == expected
+
+        errmsg = "the 'out' parameter is not supported"
+        with pytest.raises(ValueError, match=errmsg):
+            np.min(idx, out=0)
+        with pytest.raises(ValueError, match=errmsg):
+            np.max(idx, out=0)
+
+        # No need to test again argmax/argmin compat since the implementation
+        # is the same as basic integer index
+
     def test_numpy_minmax_datetime64(self):
         dr = pd.date_range(start='2016-01-15', end='2016-01-20')