diff --git a/pandas/tests/arrays/categorical/test_warnings.py b/pandas/tests/arrays/categorical/test_warnings.py
index f66c327e9967d..9e164a250cdb1 100644
--- a/pandas/tests/arrays/categorical/test_warnings.py
+++ b/pandas/tests/arrays/categorical/test_warnings.py
@@ -14,6 +14,16 @@ async def test_tab_complete_warning(self, ip):
 
         code = "import pandas as pd; c = Categorical([])"
         await ip.run_code(code)
-        with tm.assert_produces_warning(None):
+
+        # GH 31324 newer jedi version raises Deprecation warning
+        import jedi
+
+        if jedi.__version__ < "0.16.0":
+            warning = tm.assert_produces_warning(None)
+        else:
+            warning = tm.assert_produces_warning(
+                DeprecationWarning, check_stacklevel=False
+            )
+        with warning:
             with provisionalcompleter("ignore"):
                 list(ip.Completer.completions("c.", 1))
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index 1047c457d6b82..eec1ea68b55e2 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -2408,7 +2408,17 @@ async def test_tab_complete_warning(self, ip):
 
         code = "import pandas as pd; idx = pd.Index([1, 2])"
         await ip.run_code(code)
-        with tm.assert_produces_warning(None):
+
+        # GH 31324 newer jedi version raises Deprecation warning
+        import jedi
+
+        if jedi.__version__ < "0.16.0":
+            warning = tm.assert_produces_warning(None)
+        else:
+            warning = tm.assert_produces_warning(
+                DeprecationWarning, check_stacklevel=False
+            )
+        with warning:
             with provisionalcompleter("ignore"):
                 list(ip.Completer.completions("idx.", 4))