diff --git a/pandas/core/sorting.py b/pandas/core/sorting.py
index ef69939d6e978..a5d3afd38adb2 100644
--- a/pandas/core/sorting.py
+++ b/pandas/core/sorting.py
@@ -8,7 +8,9 @@
 
 from pandas.core.dtypes.cast import infer_dtype_from_array
 from pandas.core.dtypes.common import (
-    ensure_int64, ensure_platform_int, is_categorical_dtype, is_list_like)
+    ensure_int64, ensure_platform_int, is_categorical_dtype, is_list_like,
+    is_extension_array_dtype)
+from pandas.core.dtypes.generic import ABCIndexClass
 from pandas.core.dtypes.missing import isna
 
 import pandas.core.algorithms as algorithms
@@ -239,7 +241,9 @@ def nargsort(items, kind='quicksort', ascending=True, na_position='last'):
     """
 
     # specially handle Categorical
-    if is_categorical_dtype(items):
+    if is_extension_array_dtype(items):
+        if isinstance(items, ABCIndexClass):
+            items = items._values
         if na_position not in {'first', 'last'}:
             raise ValueError('invalid na_position: {!r}'.format(na_position))
 
diff --git a/pandas/tests/test_sorting.py b/pandas/tests/test_sorting.py
index 7528566e8326e..0fbc44ec27a4c 100644
--- a/pandas/tests/test_sorting.py
+++ b/pandas/tests/test_sorting.py
@@ -9,7 +9,9 @@
 
 from pandas.compat import PY2
 
-from pandas import DataFrame, MultiIndex, Series, compat, concat, merge
+from pandas import (
+    Categorical, DataFrame, MultiIndex, Series, compat,
+    concat, merge, to_datetime)
 from pandas.core import common as com
 from pandas.core.sorting import (
     decons_group_index, get_group_index, is_int64_overflow_possible,
@@ -183,6 +185,22 @@ def test_nargsort(self):
         exp = list(range(5)) + list(range(105, 110)) + list(range(104, 4, -1))
         tm.assert_numpy_array_equal(result, np.array(exp), check_dtype=False)
 
+    @pytest.mark.parametrize('data', [
+        Categorical(['a', 'c', 'a', 'b']),
+        to_datetime([0, 2, 0, 1]).tz_localize('Europe/Brussels')])
+    def test_nargsort_extension_array(self, data):
+        result = nargsort(data)
+        expected = np.array([0, 2, 3, 1], dtype=np.intp)
+        tm.assert_numpy_array_equal(result, expected)
+
+    def test_nargsort_datetimearray_warning(self, recwarn):
+        # https://github.com/pandas-dev/pandas/issues/25439
+        # can be removed once the FutureWarning for np.array(DTA) is removed
+        data = to_datetime([0, 2, 0, 1]).tz_localize('Europe/Brussels')
+        nargsort(data)
+        msg = "Converting timezone-aware DatetimeArray to timezone-naive"
+        assert len([w for w in recwarn.list if msg in str(w.message)]) == 0
+
 
 class TestMerge(object):