diff --git a/doc/source/whatsnew/v2.3.2.rst b/doc/source/whatsnew/v2.3.2.rst
index 03244c808ad03..478bd945a3735 100644
--- a/doc/source/whatsnew/v2.3.2.rst
+++ b/doc/source/whatsnew/v2.3.2.rst
@@ -25,7 +25,8 @@ Bug fixes
 - Fix :meth:`~DataFrame.to_json` with ``orient="table"`` to correctly use the
   "string" type in the JSON Table Schema for :class:`StringDtype` columns
   (:issue:`61889`)
-
+- Fixed ``~Series.str.match`` and ``~Series.str.fullmatch`` with compiled regex
+  for the Arrow-backed string dtype (:issue:`61964`)
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_232.contributors:
diff --git a/pandas/core/arrays/_arrow_string_mixins.py b/pandas/core/arrays/_arrow_string_mixins.py
index e136b4f92031d..7e9b084330111 100644
--- a/pandas/core/arrays/_arrow_string_mixins.py
+++ b/pandas/core/arrays/_arrow_string_mixins.py
@@ -301,23 +301,29 @@ def _str_contains(
 
     def _str_match(
         self,
-        pat: str,
+        pat: str | re.Pattern,
         case: bool = True,
         flags: int = 0,
         na: Scalar | lib.NoDefault = lib.no_default,
     ):
-        if not pat.startswith("^"):
+        if isinstance(pat, re.Pattern):
+            # GH#61952
+            pat = pat.pattern
+        if isinstance(pat, str) and not pat.startswith("^"):
             pat = f"^{pat}"
         return self._str_contains(pat, case, flags, na, regex=True)
 
     def _str_fullmatch(
         self,
-        pat,
+        pat: str | re.Pattern,
         case: bool = True,
         flags: int = 0,
         na: Scalar | lib.NoDefault = lib.no_default,
     ):
-        if not pat.endswith("$") or pat.endswith("\\$"):
+        if isinstance(pat, re.Pattern):
+            # GH#61952
+            pat = pat.pattern
+        if isinstance(pat, str) and (not pat.endswith("$") or pat.endswith("\\$")):
             pat = f"{pat}$"
         return self._str_match(pat, case, flags, na)
 
diff --git a/pandas/core/strings/accessor.py b/pandas/core/strings/accessor.py
index c0e458f7968e7..da17543f8470d 100644
--- a/pandas/core/strings/accessor.py
+++ b/pandas/core/strings/accessor.py
@@ -1353,8 +1353,8 @@ def match(self, pat: str, case: bool = True, flags: int = 0, na=lib.no_default):
 
         Parameters
         ----------
-        pat : str
-            Character sequence.
+        pat : str or compiled regex
+            Character sequence or regular expression.
         case : bool, default True
             If True, case sensitive.
         flags : int, default 0 (no flags)
diff --git a/pandas/core/strings/object_array.py b/pandas/core/strings/object_array.py
index e82c6c20e86d9..30696141d552b 100644
--- a/pandas/core/strings/object_array.py
+++ b/pandas/core/strings/object_array.py
@@ -245,14 +245,15 @@ def rep(x, r):
 
     def _str_match(
         self,
-        pat: str,
+        pat: str | re.Pattern,
         case: bool = True,
         flags: int = 0,
         na: Scalar | lib.NoDefault = lib.no_default,
     ):
         if not case:
             flags |= re.IGNORECASE
-
+        if isinstance(pat, re.Pattern):
+            pat = pat.pattern
         regex = re.compile(pat, flags=flags)
 
         f = lambda x: regex.match(x) is not None
@@ -267,7 +268,8 @@ def _str_fullmatch(
     ):
         if not case:
             flags |= re.IGNORECASE
-
+        if isinstance(pat, re.Pattern):
+            pat = pat.pattern
         regex = re.compile(pat, flags=flags)
 
         f = lambda x: regex.fullmatch(x) is not None
diff --git a/pandas/tests/strings/test_find_replace.py b/pandas/tests/strings/test_find_replace.py
index dfa9a36995480..2bda4b8fba434 100644
--- a/pandas/tests/strings/test_find_replace.py
+++ b/pandas/tests/strings/test_find_replace.py
@@ -822,6 +822,17 @@ def test_match_case_kwarg(any_string_dtype):
     tm.assert_series_equal(result, expected)
 
 
+def test_match_compiled_regex(any_string_dtype):
+    # GH#61952
+    values = Series(["ab", "AB", "abc", "ABC"], dtype=any_string_dtype)
+    result = values.str.match(re.compile(r"ab"), case=False)
+    expected_dtype = (
+        np.bool_ if is_object_or_nan_string_dtype(any_string_dtype) else "boolean"
+    )
+    expected = Series([True, True, True, True], dtype=expected_dtype)
+    tm.assert_series_equal(result, expected)
+
+
 # --------------------------------------------------------------------------------------
 # str.fullmatch
 # --------------------------------------------------------------------------------------
@@ -891,6 +902,17 @@ def test_fullmatch_case_kwarg(any_string_dtype):
     tm.assert_series_equal(result, expected)
 
 
+def test_fullmatch_compiled_regex(any_string_dtype):
+    # GH#61952
+    values = Series(["ab", "AB", "abc", "ABC"], dtype=any_string_dtype)
+    result = values.str.fullmatch(re.compile(r"ab"), case=False)
+    expected_dtype = (
+        np.bool_ if is_object_or_nan_string_dtype(any_string_dtype) else "boolean"
+    )
+    expected = Series([True, True, False, False], dtype=expected_dtype)
+    tm.assert_series_equal(result, expected)
+
+
 # --------------------------------------------------------------------------------------
 # str.findall
 # --------------------------------------------------------------------------------------