diff --git a/pandas/_libs/lib.pyi b/pandas/_libs/lib.pyi
index 9dbc47f1d40f7..902d1b7245b46 100644
--- a/pandas/_libs/lib.pyi
+++ b/pandas/_libs/lib.pyi
@@ -196,6 +196,7 @@ def map_infer_mask(
     convert: bool = ...,
     na_value: Any = ...,
     dtype: np.dtype = ...,
+    out: np.ndarray = ...,
 ) -> np.ndarray: ...
 
 def indices_fast(
diff --git a/pandas/_libs/lib.pyx b/pandas/_libs/lib.pyx
index e1cb744c7033c..58bd6cdc54b7d 100644
--- a/pandas/_libs/lib.pyx
+++ b/pandas/_libs/lib.pyx
@@ -2536,7 +2536,8 @@ no_default = NoDefault.no_default  # Sentinel indicating the default value.
 @cython.boundscheck(False)
 @cython.wraparound(False)
 def map_infer_mask(ndarray arr, object f, const uint8_t[:] mask, bint convert=True,
-                   object na_value=no_default, cnp.dtype dtype=np.dtype(object)
+                   object na_value=no_default, cnp.dtype dtype=np.dtype(object),
+                   ndarray out=None
                    ) -> np.ndarray:
     """
     Substitute for np.vectorize with pandas-friendly dtype inference.
@@ -2554,6 +2555,8 @@ def map_infer_mask(ndarray arr, object f, const uint8_t[:] mask, bint convert=Tr
         input value is used
     dtype : numpy.dtype
         The numpy dtype to use for the result ndarray.
+    out : ndarray
+        The result.
 
     Returns
     -------
@@ -2565,7 +2568,10 @@ def map_infer_mask(ndarray arr, object f, const uint8_t[:] mask, bint convert=Tr
         object val
 
     n = len(arr)
-    result = np.empty(n, dtype=dtype)
+    if out is not None:
+        result = out
+    else:
+        result = np.empty(n, dtype=dtype)
     for i in range(n):
         if mask[i]:
             if na_value is no_default:
diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index cb8a08f5668ac..95d9409b265ce 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -2453,7 +2453,9 @@ def replace(self, to_replace, value, inplace: bool = False):
 
     # ------------------------------------------------------------------------
     # String methods interface
-    def _str_map(self, f, na_value=np.nan, dtype=np.dtype("object")):
+    def _str_map(
+        self, f, na_value=np.nan, dtype=np.dtype("object"), convert: bool = True
+    ):
         # Optimization to apply the callable `f` to the categories once
         # and rebuild the result by `take`ing from the result with the codes.
         # Returns the same type as the object-dtype implementation though.
diff --git a/pandas/core/arrays/string_.py b/pandas/core/arrays/string_.py
index 74ca5130ca322..ab1dadf4d2dfa 100644
--- a/pandas/core/arrays/string_.py
+++ b/pandas/core/arrays/string_.py
@@ -410,7 +410,9 @@ def _cmp_method(self, other, op):
     # String methods interface
     _str_na_value = StringDtype.na_value
 
-    def _str_map(self, f, na_value=None, dtype: Dtype | None = None):
+    def _str_map(
+        self, f, na_value=None, dtype: Dtype | None = None, convert: bool = True
+    ):
         from pandas.arrays import BooleanArray
 
         if dtype is None:
diff --git a/pandas/core/arrays/string_arrow.py b/pandas/core/arrays/string_arrow.py
index d5ee28eb7017e..1e2f382b2976f 100644
--- a/pandas/core/arrays/string_arrow.py
+++ b/pandas/core/arrays/string_arrow.py
@@ -741,7 +741,9 @@ def value_counts(self, dropna: bool = True) -> Series:
 
     _str_na_value = ArrowStringDtype.na_value
 
-    def _str_map(self, f, na_value=None, dtype: Dtype | None = None):
+    def _str_map(
+        self, f, na_value=None, dtype: Dtype | None = None, convert: bool = True
+    ):
         # TODO: de-duplicate with StringArray method. This method is moreless copy and
         # paste.
 
diff --git a/pandas/core/strings/accessor.py b/pandas/core/strings/accessor.py
index 43df34a7ecbb2..a56c62074cc2a 100644
--- a/pandas/core/strings/accessor.py
+++ b/pandas/core/strings/accessor.py
@@ -15,10 +15,7 @@
 import numpy as np
 
 import pandas._libs.lib as lib
-from pandas._typing import (
-    ArrayLike,
-    FrameOrSeriesUnion,
-)
+from pandas._typing import FrameOrSeriesUnion
 from pandas.util._decorators import Appender
 
 from pandas.core.dtypes.common import (
@@ -162,7 +159,6 @@ class StringMethods(NoNewAttributesMixin):
     # TODO: Dispatch all the methods
     # Currently the following are not dispatched to the array
     # * cat
-    # * extract
     # * extractall
 
     def __init__(self, data):
@@ -245,7 +241,7 @@ def _wrap_result(
         self,
         result,
         name=None,
-        expand=None,
+        expand: Optional[bool] = None,
         fill_value=np.nan,
         returns_string=True,
     ):
@@ -2383,8 +2379,36 @@ def extract(
         if not expand and regex.groups > 1 and isinstance(self._data, ABCIndex):
             raise ValueError("only one regex group is supported with Index")
 
-        # TODO: dispatch
-        return str_extract(self, pat, flags, expand=expand)
+        result = self._data.array._str_extract(pat, flags, expand)
+        returns_df = regex.groups > 1 or expand
+
+        name = _get_group_names(regex) if returns_df else _get_single_group_name(regex)
+
+        # extract is inconsistent for Indexes when expand is True. To avoid special
+        # casing _wrap_result we handle that case here
+        if expand and isinstance(self._data, ABCIndex):
+            from pandas import DataFrame
+
+            # if expand is True, name is a list of column names
+            assert isinstance(name, list)  # for mypy
+            return DataFrame(result, columns=name, dtype=object)
+
+        # bypass padding code in _wrap_result
+        expand_kwarg: Optional[bool]
+        if returns_df:
+            if is_object_dtype(result):
+                if regex.groups == 1:
+                    result = result.reshape(1, -1).T
+                if result.size == 0:
+                    expand_kwarg = True
+                else:
+                    expand_kwarg = None
+            else:
+                expand_kwarg = True
+        else:
+            expand_kwarg = False
+
+        return self._wrap_result(result, name=name, expand=expand_kwarg)
 
     @forbid_nonstring_types(["bytes"])
     def extractall(self, pat, flags=0):
@@ -3071,72 +3095,6 @@ def _get_group_names(regex: Pattern) -> List[Hashable]:
     return [names.get(1 + i, i) for i in range(regex.groups)]
 
 
-def _str_extract(arr: ArrayLike, pat: str, flags=0, expand: bool = True):
-    """
-    Find groups in each string in the array using passed regular expression.
-
-    Returns
-    -------
-    np.ndarray or list of lists is expand is True
-    """
-    regex = re.compile(pat, flags=flags)
-
-    empty_row = [np.nan] * regex.groups
-
-    def f(x):
-        if not isinstance(x, str):
-            return empty_row
-        m = regex.search(x)
-        if m:
-            return [np.nan if item is None else item for item in m.groups()]
-        else:
-            return empty_row
-
-    if expand:
-        return [f(val) for val in np.asarray(arr)]
-
-    return np.array([f(val)[0] for val in np.asarray(arr)], dtype=object)
-
-
-def str_extract(accessor: StringMethods, pat: str, flags: int = 0, expand: bool = True):
-    from pandas import (
-        DataFrame,
-        array as pd_array,
-    )
-
-    obj = accessor._data
-    result_dtype = _result_dtype(obj)
-    regex = re.compile(pat, flags=flags)
-    returns_df = regex.groups > 1 or expand
-
-    if returns_df:
-        name = None
-        columns = _get_group_names(regex)
-
-        if obj.array.size == 0:
-            result = DataFrame(columns=columns, dtype=result_dtype)
-
-        else:
-            result_list = _str_extract(obj.array, pat, flags=flags, expand=returns_df)
-
-            result_index: Optional["Index"]
-            if isinstance(obj, ABCSeries):
-                result_index = obj.index
-            else:
-                result_index = None
-
-            result = DataFrame(
-                result_list, columns=columns, index=result_index, dtype=result_dtype
-            )
-
-    else:
-        name = _get_single_group_name(regex)
-        result_arr = _str_extract(obj.array, pat, flags=flags, expand=returns_df)
-        # not dispatching, so we have to reconstruct here.
-        result = pd_array(result_arr, dtype=result_dtype)
-    return accessor._wrap_result(result, name=name)
-
-
 def str_extractall(arr, pat, flags=0):
     regex = re.compile(pat, flags=flags)
     # the regex must contain capture groups.
diff --git a/pandas/core/strings/base.py b/pandas/core/strings/base.py
index a77f8861a7c02..9cd0f25c1055a 100644
--- a/pandas/core/strings/base.py
+++ b/pandas/core/strings/base.py
@@ -222,3 +222,7 @@ def _str_split(self, pat=None, n=-1, expand=False):
     @abc.abstractmethod
     def _str_rsplit(self, pat=None, n=-1):
         pass
+
+    @abc.abstractmethod
+    def _str_extract(self, pat: str, flags: int = 0, expand: bool = True):
+        pass
diff --git a/pandas/core/strings/object_array.py b/pandas/core/strings/object_array.py
index 869eabc76b555..0f54d5f869973 100644
--- a/pandas/core/strings/object_array.py
+++ b/pandas/core/strings/object_array.py
@@ -19,6 +19,7 @@
 )
 
 from pandas.core.dtypes.common import (
+    is_object_dtype,
     is_re,
     is_scalar,
 )
@@ -38,7 +39,9 @@ def __len__(self):
         # For typing, _str_map relies on the object being sized.
         raise NotImplementedError
 
-    def _str_map(self, f, na_value=None, dtype: Optional[Dtype] = None):
+    def _str_map(
+        self, f, na_value=None, dtype: Optional[Dtype] = None, convert: bool = True
+    ):
         """
         Map a callable over valid element of the array.
 
@@ -53,6 +56,8 @@ def _str_map(self, f, na_value=None, dtype: Optional[Dtype] = None):
             for object-dtype and Categorical and ``pd.NA`` for StringArray.
         dtype : Dtype, optional
             The dtype of the result array.
+        convert : bool, default True
+            Whether to call `maybe_convert_objects` on the resulting ndarray
         """
         if dtype is None:
             dtype = np.dtype("object")
@@ -66,9 +71,9 @@ def _str_map(self, f, na_value=None, dtype: Optional[Dtype] = None):
 
         arr = np.asarray(self, dtype=object)
         mask = isna(arr)
-        convert = not np.all(mask)
+        map_convert = convert and not np.all(mask)
         try:
-            result = lib.map_infer_mask(arr, f, mask.view(np.uint8), convert)
+            result = lib.map_infer_mask(arr, f, mask.view(np.uint8), map_convert)
         except (TypeError, AttributeError) as e:
             # Reraise the exception if callable `f` got wrong number of args.
             # The user may want to be warned by this, instead of getting NaN
@@ -94,7 +99,7 @@ def g(x):
             return result
         if na_value is not np.nan:
             np.putmask(result, mask, na_value)
-            if result.dtype == object:
+            if convert and result.dtype == object:
                 result = lib.maybe_convert_objects(result)
         return result
 
@@ -408,3 +413,51 @@ def _str_lstrip(self, to_strip=None):
 
     def _str_rstrip(self, to_strip=None):
         return self._str_map(lambda x: x.rstrip(to_strip))
+
+    def _str_extract(self, pat: str, flags: int = 0, expand: bool = True):
+        regex = re.compile(pat, flags=flags)
+        na_value = self._str_na_value
+
+        if regex.groups == 1:
+
+            def f(x):
+                m = regex.search(x)
+                return m.groups()[0] if m else na_value
+
+            return self._str_map(f, convert=False)
+        else:
+            out = np.empty((len(self), regex.groups), dtype=object)
+
+            if is_object_dtype(self):
+
+                def f(x):
+                    if not isinstance(x, str):
+                        return na_value
+                    m = regex.search(x)
+                    if m:
+                        return [
+                            na_value if item is None else item for item in m.groups()
+                        ]
+                    else:
+                        return na_value
+
+            else:
+
+                def f(x):
+                    m = regex.search(x)
+                    if m:
+                        return [
+                            na_value if item is None else item for item in m.groups()
+                        ]
+                    else:
+                        return na_value
+
+            result = lib.map_infer_mask(
+                np.asarray(self),
+                f,
+                mask=isna(self).view("uint8"),
+                convert=False,
+                na_value=na_value,
+                out=out,
+            )
+            return result