diff --git a/pandas/tests/io/formats/test_format.py b/pandas/tests/io/formats/test_format.py
index a7c9c86b3d9a5..36e8e9d2264f5 100644
--- a/pandas/tests/io/formats/test_format.py
+++ b/pandas/tests/io/formats/test_format.py
@@ -19,6 +19,9 @@
 
 from pandas.compat import (
     IS64,
+    PY310,
+    PY311,
+    is_numpy_dev,
     is_platform_windows,
 )
 import pandas.util._test_decorators as td
@@ -3384,10 +3387,23 @@ def test_filepath_or_buffer_arg(
         ):
             getattr(df, method)(buf=filepath_or_buffer, encoding=encoding)
     elif encoding == "foo":
-        expected_warning = FutureWarning if method == "to_latex" else None
-        with tm.assert_produces_warning(expected_warning):
-            with pytest.raises(LookupError, match="unknown encoding"):
-                getattr(df, method)(buf=filepath_or_buffer, encoding=encoding)
+        if (
+            method == "to_string"
+            and data == "abc"
+            and filepath_or_buffer_id == "string"
+            and PY310
+            and not PY311
+            and not is_numpy_dev
+        ):
+            # raises importwarning _SixMetaPathImporter.find_spec
+            with tm.assert_produces_warning(ImportWarning, check_stacklevel=False):
+                with pytest.raises(LookupError, match="unknown encoding"):
+                    getattr(df, method)(buf=filepath_or_buffer, encoding=encoding)
+        else:
+            expected_warning = FutureWarning if method == "to_latex" else None
+            with tm.assert_produces_warning(expected_warning):
+                with pytest.raises(LookupError, match="unknown encoding"):
+                    getattr(df, method)(buf=filepath_or_buffer, encoding=encoding)
     else:
         expected = getattr(df, method)()
         getattr(df, method)(buf=filepath_or_buffer, encoding=encoding)