diff --git a/pandas/core/arrays/string_.py b/pandas/core/arrays/string_.py
index de129df2575d3..b92504fe507cd 100644
--- a/pandas/core/arrays/string_.py
+++ b/pandas/core/arrays/string_.py
@@ -28,7 +28,10 @@
     pa_version_under10p1,
 )
 from pandas.compat.numpy import function as nv
-from pandas.util._decorators import doc
+from pandas.util._decorators import (
+    doc,
+    set_module,
+)
 from pandas.util._exceptions import find_stack_level
 
 from pandas.core.dtypes.base import (
@@ -86,6 +89,7 @@
     from pandas import Series
 
 
+@set_module("pandas")
 @register_extension_dtype
 class StringDtype(StorageExtensionDtype):
     """
@@ -374,6 +378,7 @@ def __from_arrow__(
         return new_string_array
 
 
+@set_module("pandas")
 class BaseStringArray(ExtensionArray):
     """
     Mixin class for StringArray, ArrowStringArray.
@@ -532,6 +537,8 @@ def _str_map_nan_semantics(
 
 # error: Definition of "_concat_same_type" in base class "NDArrayBacked" is
 # incompatible with definition in base class "ExtensionArray"
+
+
 class StringArray(BaseStringArray, NumpyExtensionArray):  # type: ignore[misc]
     """
     Extension array for string data.
@@ -721,7 +728,8 @@ def __arrow_array__(self, type=None):
         values[self.isna()] = None
         return pa.array(values, type=type, from_pandas=True)
 
-    def _values_for_factorize(self) -> tuple[np.ndarray, libmissing.NAType | float]:  # type: ignore[override]
+    # type: ignore[override]
+    def _values_for_factorize(self) -> tuple[np.ndarray, libmissing.NAType | float]:
         arr = self._ndarray
 
         return arr, self.dtype.na_value
diff --git a/pandas/tests/api/test_api.py b/pandas/tests/api/test_api.py
index 842fa1a151267..68650e24f8d19 100644
--- a/pandas/tests/api/test_api.py
+++ b/pandas/tests/api/test_api.py
@@ -416,3 +416,7 @@ def test_set_module():
     assert pd.Period.__module__ == "pandas"
     assert pd.Timestamp.__module__ == "pandas"
     assert pd.Timedelta.__module__ == "pandas"
+    assert pd.StringDtype.__module__ == "pandas"
+    assert pd.BaseStringArray.__module__ == "pandas"
+    assert pd.StringArrayNumpySemantics.___module__ == "pandas"
+    assert pd.StringArray.__module__ == "pandas"