diff --git a/xarray/core/indexing.py b/xarray/core/indexing.py
index 67912908a2b..6985d6681a5 100644
--- a/xarray/core/indexing.py
+++ b/xarray/core/indexing.py
@@ -875,10 +875,10 @@ def as_indexable(array):
         return PandasIndexingAdapter(array)
     if is_duck_dask_array(array):
         return DaskIndexingAdapter(array)
-    if hasattr(array, "__array_function__"):
-        return NdArrayLikeIndexingAdapter(array)
     if hasattr(array, "__array_namespace__"):
         return ArrayApiIndexingAdapter(array)
+    if hasattr(array, "__array_function__"):
+        return NdArrayLikeIndexingAdapter(array)
 
     raise TypeError(f"Invalid array type: {type(array)}")
 
diff --git a/xarray/tests/test_indexing.py b/xarray/tests/test_indexing.py
index 39ac09bf802..4bf05471d71 100644
--- a/xarray/tests/test_indexing.py
+++ b/xarray/tests/test_indexing.py
@@ -904,6 +904,14 @@ def __array_function__(self, func, types, args, kwargs):
         pass
 
 
+class ArrayWithNamespaceAndArrayFunction:
+    def __array_namespace__(self, version=None):
+        pass
+
+    def __array_function__(self, func, types, args, kwargs):
+        pass
+
+
 @pytest.mark.parametrize(
     ["array", "expected_type"],
     (
@@ -926,6 +934,11 @@ def __array_function__(self, func, types, args, kwargs):
             indexing.NdArrayLikeIndexingAdapter,
             id="array_like",
         ),
+        pytest.param(
+            ArrayWithNamespaceAndArrayFunction(),
+            indexing.ArrayApiIndexingAdapter,
+            id="array_api_with_fallback",
+        ),
     ),
 )
 def test_as_indexable(array, expected_type):