diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 29f360e050548..08ba7d80f6880 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -1089,7 +1089,7 @@ Performance improvements
 - Performance improvement in :meth:`Series.rank` for pyarrow-backed dtypes (:issue:`50264`)
 - Performance improvement in :meth:`Series.searchsorted` for pyarrow-backed dtypes (:issue:`50447`)
 - Performance improvement in :meth:`Series.fillna` for extension array dtypes (:issue:`49722`, :issue:`50078`)
-- Performance improvement in :meth:`Index.join`, :meth:`Index.intersection` and :meth:`Index.union` for masked dtypes when :class:`Index` is monotonic (:issue:`50310`)
+- Performance improvement in :meth:`Index.join`, :meth:`Index.intersection` and :meth:`Index.union` for masked and arrow dtypes when :class:`Index` is monotonic (:issue:`50310`, :issue:`51365`)
 - Performance improvement for :meth:`Series.value_counts` with nullable dtype (:issue:`48338`)
 - Performance improvement for :class:`Series` constructor passing integer numpy array with nullable dtype (:issue:`48338`)
 - Performance improvement for :class:`DatetimeIndex` constructor passing a list (:issue:`48609`)
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 363bfe76d40fb..9d4a4ca8a5140 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -145,6 +145,7 @@
     validate_putmask,
 )
 from pandas.core.arrays import (
+    ArrowExtensionArray,
     BaseMaskedArray,
     Categorical,
     ExtensionArray,
@@ -4847,8 +4848,10 @@ def _can_use_libjoin(self) -> bool:
         if type(self) is Index:
             # excludes EAs, but include masks, we get here with monotonic
             # values only, meaning no NA
-            return isinstance(self.dtype, np.dtype) or isinstance(
-                self.values, BaseMaskedArray
+            return (
+                isinstance(self.dtype, np.dtype)
+                or isinstance(self.values, BaseMaskedArray)
+                or isinstance(self._values, ArrowExtensionArray)
             )
         return not is_interval_dtype(self.dtype)
 
@@ -4939,6 +4942,10 @@ def _get_join_target(self) -> ArrayLike:
         if isinstance(self._values, BaseMaskedArray):
             # This is only used if our array is monotonic, so no NAs present
             return self._values._data
+        elif isinstance(self._values, ArrowExtensionArray):
+            # This is only used if our array is monotonic, so no missing values
+            # present
+            return self._values.to_numpy()
         return self._get_engine_target()
 
     def _from_join_target(self, result: np.ndarray) -> ArrayLike:
@@ -4948,6 +4955,8 @@ def _from_join_target(self, result: np.ndarray) -> ArrayLike:
         """
         if isinstance(self.values, BaseMaskedArray):
             return type(self.values)(result, np.zeros(result.shape, dtype=np.bool_))
+        elif isinstance(self.values, ArrowExtensionArray):
+            return type(self.values)._from_sequence(result)
         return result
 
     @doc(IndexOpsMixin._memory_usage)
diff --git a/pandas/tests/indexes/test_setops.py b/pandas/tests/indexes/test_setops.py
index 001efe07b5d2b..708de02518b73 100644
--- a/pandas/tests/indexes/test_setops.py
+++ b/pandas/tests/indexes/test_setops.py
@@ -886,3 +886,11 @@ def test_symmetric_difference_non_index(self, sort):
         result = index1.symmetric_difference(index2, result_name="new_name", sort=sort)
         assert tm.equalContents(result, expected)
         assert result.name == "new_name"
+
+    def test_union_ea_dtypes(self, any_numeric_ea_and_arrow_dtype):
+        # GH#51365
+        idx = Index([1, 2, 3], dtype=any_numeric_ea_and_arrow_dtype)
+        idx2 = Index([3, 4, 5], dtype=any_numeric_ea_and_arrow_dtype)
+        result = idx.union(idx2)
+        expected = Index([1, 2, 3, 4, 5], dtype=any_numeric_ea_and_arrow_dtype)
+        tm.assert_index_equal(result, expected)