diff --git a/pandas/core/strings/accessor.py b/pandas/core/strings/accessor.py
index 15fc2d9e6d3c5..5606380908f38 100644
--- a/pandas/core/strings/accessor.py
+++ b/pandas/core/strings/accessor.py
@@ -3086,52 +3086,38 @@ def _get_group_names(regex: Pattern) -> List[Hashable]:
 
 def _str_extract_noexpand(arr, pat, flags=0):
     """
-    Find groups in each string in the Series using passed regular
-    expression. This function is called from
-    str_extract(expand=False), and can return Series, DataFrame, or
-    Index.
+    Find groups in each string in the Series/Index using passed regular expression.
 
+    This function is called from str_extract(expand=False) when there is a single group
+    in the regex.
+
+    Returns
+    -------
+    np.ndarray
     """
-    from pandas import (
-        DataFrame,
-        array as pd_array,
-    )
+    from pandas import array as pd_array
 
     regex = re.compile(pat, flags=flags)
     groups_or_na = _groups_or_na_fun(regex)
     result_dtype = _result_dtype(arr)
 
-    if regex.groups == 1:
-        result = np.array([groups_or_na(val)[0] for val in arr], dtype=object)
-        name = _get_single_group_name(regex)
-        # not dispatching, so we have to reconstruct here.
-        result = pd_array(result, dtype=result_dtype)
-    else:
-        name = None
-        columns = _get_group_names(regex)
-        if arr.size == 0:
-            # error: Incompatible types in assignment (expression has type
-            # "DataFrame", variable has type "ndarray")
-            result = DataFrame(  # type: ignore[assignment]
-                columns=columns, dtype=result_dtype
-            )
-        else:
-            # error: Incompatible types in assignment (expression has type
-            # "DataFrame", variable has type "ndarray")
-            result = DataFrame(  # type:ignore[assignment]
-                [groups_or_na(val) for val in arr],
-                columns=columns,
-                index=arr.index,
-                dtype=result_dtype,
-            )
-    return result, name
+    result = np.array([groups_or_na(val)[0] for val in arr], dtype=object)
+    # not dispatching, so we have to reconstruct here.
+    result = pd_array(result, dtype=result_dtype)
+    return result
 
 
 def _str_extract_frame(arr, pat, flags=0):
     """
-    For each subject string in the Series, extract groups from the
-    first match of regular expression pat. This function is called from
-    str_extract(expand=True), and always returns a DataFrame.
+    Find groups in each string in the Series/Index using passed regular expression.
+
+    For each subject string in the Series/Index, extract groups from the first match of
+    regular expression pat. This function is called from str_extract(expand=True) or
+    str_extract(expand=False) when there is more than one group in the regex.
+
+    Returns
+    -------
+    DataFrame
 
     """
     from pandas import DataFrame
@@ -3141,11 +3127,13 @@ def _str_extract_frame(arr, pat, flags=0):
     columns = _get_group_names(regex)
     result_dtype = _result_dtype(arr)
 
-    if len(arr) == 0:
+    if arr.size == 0:
         return DataFrame(columns=columns, dtype=result_dtype)
-    try:
+
+    result_index: Optional["Index"]
+    if isinstance(arr, ABCSeries):
         result_index = arr.index
-    except AttributeError:
+    else:
         result_index = None
     return DataFrame(
         [groups_or_na(val) for val in arr],
@@ -3156,12 +3144,16 @@ def _str_extract_frame(arr, pat, flags=0):
 
 
 def str_extract(arr, pat, flags=0, expand=True):
-    if expand:
+    regex = re.compile(pat, flags=flags)
+    returns_df = regex.groups > 1 or expand
+
+    if returns_df:
+        name = None
         result = _str_extract_frame(arr._orig, pat, flags=flags)
-        return result.__finalize__(arr._orig, method="str_extract")
     else:
-        result, name = _str_extract_noexpand(arr._orig, pat, flags=flags)
-        return arr._wrap_result(result, name=name, expand=expand)
+        name = _get_single_group_name(regex)
+        result = _str_extract_noexpand(arr._orig, pat, flags=flags)
+    return arr._wrap_result(result, name=name)
 
 
 def str_extractall(arr, pat, flags=0):