diff --git a/pandas/compat/__init__.py b/pandas/compat/__init__.py
index 1c08df80df477..caa00b205a29c 100644
--- a/pandas/compat/__init__.py
+++ b/pandas/compat/__init__.py
@@ -31,6 +31,7 @@
     pa_version_under13p0,
     pa_version_under14p0,
     pa_version_under14p1,
+    pa_version_under16p0,
 )
 
 if TYPE_CHECKING:
@@ -187,6 +188,7 @@ def get_bz2_file() -> type[pandas.compat.compressors.BZ2File]:
     "pa_version_under13p0",
     "pa_version_under14p0",
     "pa_version_under14p1",
+    "pa_version_under16p0",
     "IS64",
     "ISMUSL",
     "PY310",
diff --git a/pandas/compat/pyarrow.py b/pandas/compat/pyarrow.py
index 5c9e885f8e9f5..5a96e5a4cc49a 100644
--- a/pandas/compat/pyarrow.py
+++ b/pandas/compat/pyarrow.py
@@ -15,6 +15,7 @@
     pa_version_under14p0 = _palv < Version("14.0.0")
     pa_version_under14p1 = _palv < Version("14.0.1")
     pa_version_under15p0 = _palv < Version("15.0.0")
+    pa_version_under16p0 = _palv < Version("16.0.0")
 except ImportError:
     pa_version_under10p1 = True
     pa_version_under11p0 = True
@@ -23,3 +24,4 @@
     pa_version_under14p0 = True
     pa_version_under14p1 = True
     pa_version_under15p0 = True
+    pa_version_under16p0 = True
diff --git a/pandas/tests/indexes/object/test_indexing.py b/pandas/tests/indexes/object/test_indexing.py
index 039836da75cd5..34cc8eab4d812 100644
--- a/pandas/tests/indexes/object/test_indexing.py
+++ b/pandas/tests/indexes/object/test_indexing.py
@@ -7,6 +7,7 @@
     NA,
     is_matching_na,
 )
+from pandas.compat import pa_version_under16p0
 import pandas.util._test_decorators as td
 
 import pandas as pd
@@ -201,7 +202,16 @@ class TestSliceLocs:
             (pd.IndexSlice["m":"m":-1], ""),  # type: ignore[misc]
         ],
     )
-    def test_slice_locs_negative_step(self, in_slice, expected, dtype):
+    def test_slice_locs_negative_step(self, in_slice, expected, dtype, request):
+        if (
+            not pa_version_under16p0
+            and dtype == "string[pyarrow_numpy]"
+            and in_slice == slice("a", "a", -1)
+        ):
+            request.applymarker(
+                pytest.mark.xfail(reason="https://github.com/apache/arrow/issues/40642")
+            )
+
         index = Index(list("bcdxy"), dtype=dtype)
 
         s_start, s_stop = index.slice_locs(in_slice.start, in_slice.stop, in_slice.step)