diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index c18f06c3a126d..bf9a53a5490f9 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -1478,7 +1478,13 @@ def to_numpy(
         return result
 
     def map(self, mapper, na_action: Literal["ignore"] | None = None):
-        if is_numeric_dtype(self.dtype):
+        if not is_string_dtype(self.dtype) and any(
+            [
+                is_numeric_dtype(self.dtype)
+                or pa.types.is_date(self.dtype.pyarrow_dtype)
+                or pa.types.is_timestamp(self.dtype.pyarrow_dtype)
+            ]
+        ):
             return map_array(self.to_numpy(), mapper, na_action=na_action)
         else:
             return super().map(mapper, na_action)