diff --git a/doc/source/whatsnew/v2.3.3.rst b/doc/source/whatsnew/v2.3.3.rst
index aaed7544d9975..1184835ff3a1a 100644
--- a/doc/source/whatsnew/v2.3.3.rst
+++ b/doc/source/whatsnew/v2.3.3.rst
@@ -25,6 +25,7 @@ Bug fixes
 - Fix bug in :meth:`Series.str.replace` using named capture groups (e.g., ``\g<name>``) with the Arrow-backed dtype would raise an error (:issue:`57636`)
 - Fix regression in ``~Series.str.contains``, ``~Series.str.match`` and ``~Series.str.fullmatch``
   with a compiled regex and custom flags (:issue:`62240`)
+- Fix :meth:`Series.str.fullmatch` not matching patterns with groups correctly for the Arrow-backed string dtype (:issue:`61072`)
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_233.contributors:
diff --git a/pandas/core/arrays/_arrow_string_mixins.py b/pandas/core/arrays/_arrow_string_mixins.py
index 74c59dd465b52..f6867934327b0 100644
--- a/pandas/core/arrays/_arrow_string_mixins.py
+++ b/pandas/core/arrays/_arrow_string_mixins.py
@@ -327,8 +327,12 @@ def _str_fullmatch(
         flags: int = 0,
         na: Scalar | lib.NoDefault = lib.no_default,
     ):
-        if not pat.endswith("$") or pat.endswith("\\$"):
-            pat = f"{pat}$"
+        if (not pat.endswith("$") or pat.endswith("\\$")) and not pat.startswith("^"):
+            pat = f"^({pat})$"
+        elif not pat.endswith("$") or pat.endswith("\\$"):
+            pat = f"^({pat[1:]})$"
+        elif not pat.startswith("^"):
+            pat = f"^({pat[0:-1]})$"
         return self._str_match(pat, case, flags, na)
 
     def _str_find(self, sub: str, start: int = 0, end: int | None = None):
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index 820425ab51949..479497497a2ea 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -1876,23 +1876,28 @@ def test_str_match(pat, case, na, exp):
 
 @pytest.mark.parametrize(
     "pat, case, na, exp",
+    # Note: keep cases in sync with
+    # pandas/tests/strings/test_find_replace.py::test_str_fullmatch_extra_cases
     [
-        ["abc", False, None, [True, True, False, None]],
+        ["abc", False, None, [True, False, False, None]],
         ["Abc", True, None, [False, False, False, None]],
         ["bc", True, None, [False, False, False, None]],
-        ["ab", False, None, [True, True, False, None]],
-        ["a[a-z]{2}", False, None, [True, True, False, None]],
+        ["ab", False, None, [False, False, False, None]],
+        ["a[a-z]{2}", False, None, [True, False, False, None]],
         ["A[a-z]{1}", True, None, [False, False, False, None]],
         # GH Issue: #56652
         ["abc$", False, None, [True, False, False, None]],
         ["abc\\$", False, None, [False, True, False, None]],
         ["Abc$", True, None, [False, False, False, None]],
         ["Abc\\$", True, None, [False, False, False, None]],
+        # https://github.com/pandas-dev/pandas/issues/61072
+        ["(abc)|(abx)", True, None, [True, False, False, None]],
+        ["((abc)|(abx))", True, None, [True, False, False, None]],
     ],
 )
 def test_str_fullmatch(pat, case, na, exp):
     ser = pd.Series(["abc", "abc$", "$abc", None], dtype=ArrowDtype(pa.string()))
-    result = ser.str.match(pat, case=case, na=na)
+    result = ser.str.fullmatch(pat, case=case, na=na)
     expected = pd.Series(exp, dtype=ArrowDtype(pa.bool_()))
     tm.assert_series_equal(result, expected)
 
diff --git a/pandas/tests/strings/test_find_replace.py b/pandas/tests/strings/test_find_replace.py
index be59bc195b387..c0dbe9cf8ac5f 100644
--- a/pandas/tests/strings/test_find_replace.py
+++ b/pandas/tests/strings/test_find_replace.py
@@ -1079,6 +1079,44 @@ def test_fullmatch_compiled_regex(any_string_dtype):
         values.str.fullmatch(re.compile("ab"), flags=re.IGNORECASE)
 
 
+@pytest.mark.parametrize(
+    "pat, case, na, exp",
+    # Note: keep cases in sync with
+    # pandas/tests/extension/test_arrow.py::test_str_fullmatch
+    [
+        ["abc", False, None, [True, False, False, None]],
+        ["Abc", True, None, [False, False, False, None]],
+        ["bc", True, None, [False, False, False, None]],
+        ["ab", False, None, [False, False, False, None]],
+        ["a[a-z]{2}", False, None, [True, False, False, None]],
+        ["A[a-z]{1}", True, None, [False, False, False, None]],
+        # GH Issue: #56652
+        ["abc$", False, None, [True, False, False, None]],
+        ["abc\\$", False, None, [False, True, False, None]],
+        ["Abc$", True, None, [False, False, False, None]],
+        ["Abc\\$", True, None, [False, False, False, None]],
+        # https://github.com/pandas-dev/pandas/issues/61072
+        ["(abc)|(abx)", True, None, [True, False, False, None]],
+        ["((abc)|(abx))", True, None, [True, False, False, None]],
+    ],
+)
+def test_str_fullmatch_extra_cases(any_string_dtype, pat, case, na, exp):
+    ser = Series(["abc", "abc$", "$abc", None], dtype=any_string_dtype)
+    result = ser.str.fullmatch(pat, case=case, na=na)
+
+    if any_string_dtype == "str":
+        # NaN propagates as False
+        exp[-1] = False
+        expected_dtype = bool
+    else:
+        expected_dtype = (
+            "object" if is_object_or_nan_string_dtype(any_string_dtype) else "boolean"
+        )
+        expected = Series([True, False, np.nan, False], dtype=expected_dtype)
+    expected = Series(exp, dtype=expected_dtype)
+    tm.assert_series_equal(result, expected)
+
+
 # --------------------------------------------------------------------------------------
 # str.findall
 # --------------------------------------------------------------------------------------