diff --git a/.gitignore b/.gitignore
index d951f3fb9cbad..03f035db527fe 100644
--- a/.gitignore
+++ b/.gitignore
@@ -141,3 +141,6 @@ doc/source/savefig/
 # Pyodide/WASM related files #
 ##############################
 /.pyodide-xbuildenv-*
+
+local.py
+.venv/
diff --git a/doc/source/reference/extensions.rst b/doc/source/reference/extensions.rst
index e412793a328a3..ff93a3fd25104 100644
--- a/doc/source/reference/extensions.rst
+++ b/doc/source/reference/extensions.rst
@@ -58,6 +58,7 @@ objects.
       api.extensions.ExtensionArray.isin
       api.extensions.ExtensionArray.isna
       api.extensions.ExtensionArray.ravel
+      api.extensions.ExtensionArray.map
       api.extensions.ExtensionArray.repeat
       api.extensions.ExtensionArray.searchsorted
       api.extensions.ExtensionArray.shift
diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index 653a900fbfe45..bb6a19536f427 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -1612,15 +1612,20 @@ def to_numpy(
             result[~mask] = data[~mask]._pa_array.to_numpy()
         return result
 
-    def map(self, mapper, na_action: Literal["ignore"] | None = None):
+    def map(self, mapper,
+            na_action: Literal["ignore"] | None = None,
+            preserve_dtype: bool = False):
         if is_numeric_dtype(self.dtype):
-            return map_array(self.to_numpy(), mapper, na_action=na_action)
+            result = map_array(self.to_numpy(), mapper, na_action=na_action)
+            if preserve_dtype:
+                result = self._cast_pointwise_result(result)
+            return result
         else:
             # For "mM" cases, the super() method passes `self` without the
             #  to_numpy call, which inside map_array casts to ndarray[object].
             #  Without the to_numpy() call, NA is preserved instead of changed
             #  to None.
-            return super().map(mapper, na_action)
+            return super().map(mapper, na_action, preserve_dtype=preserve_dtype)
 
     @doc(ExtensionArray.duplicated)
     def duplicated(
diff --git a/pandas/core/arrays/base.py b/pandas/core/arrays/base.py
index 07c297b2c15ff..c37ee6c98079c 100644
--- a/pandas/core/arrays/base.py
+++ b/pandas/core/arrays/base.py
@@ -2516,7 +2516,12 @@ def __array_ufunc__(self, ufunc: np.ufunc, method: str, *inputs, **kwargs):
 
         return arraylike.default_array_ufunc(self, ufunc, method, *inputs, **kwargs)
 
-    def map(self, mapper, na_action: Literal["ignore"] | None = None):
+    def map(
+        self,
+        mapper,
+        na_action: Literal["ignore"] | None = None,
+        preserve_dtype: bool = False,
+    ):
         """
         Map values using an input mapping or function.
 
@@ -2528,6 +2533,12 @@ def map(self, mapper, na_action: Literal["ignore"] | None = None):
             If 'ignore', propagate NA values, without passing them to the
             mapping correspondence. If 'ignore' is not supported, a
             ``NotImplementedError`` should be raised.
+        preserve_dtype : bool, default False
+            If True, attempt to cast the elementwise result back to the
+            original ExtensionArray type (and dtype) when possible. This is
+            primarily intended for identity or dtype-preserving mappings.
+            If False, the result of the mapping is returned as produced by
+            the underlying implementation (typically a NumPy ndarray).
 
         Returns
         -------
@@ -2536,7 +2547,10 @@ def map(self, mapper, na_action: Literal["ignore"] | None = None):
             If the function returns a tuple with more than one element
             a MultiIndex will be returned.
         """
-        return map_array(self, mapper, na_action=na_action)
+        results = map_array(self, mapper, na_action=na_action)
+        if preserve_dtype:
+            results = self._cast_pointwise_result(results)
+        return results
 
     # ------------------------------------------------------------------------
     # GroupBy Methods
diff --git a/pandas/core/arrays/masked.py b/pandas/core/arrays/masked.py
index b00e362e1309a..9d0ee3f833218 100644
--- a/pandas/core/arrays/masked.py
+++ b/pandas/core/arrays/masked.py
@@ -1395,8 +1395,17 @@ def max(self, *, skipna: bool = True, axis: AxisInt | None = 0, **kwargs):
         )
         return self._wrap_reduction_result("max", result, skipna=skipna, axis=axis)
 
-    def map(self, mapper, na_action: Literal["ignore"] | None = None):
-        return map_array(self.to_numpy(), mapper, na_action=na_action)
+    def map(
+        self,
+        mapper,
+        na_action: Literal["ignore"] | None = None,
+        preserve_dtype: bool = False,
+    ):
+        """See ExtensionArray.map."""
+        result = map_array(self.to_numpy(), mapper, na_action=na_action)
+        if preserve_dtype:
+            result = self._cast_pointwise_result(result)
+        return result
 
     @overload
     def any(