diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index 3569a578943d4..4e0cc93e64458 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -948,7 +948,7 @@ def value_counts_internal(
             result = Series(counts, index=idx, name=name, copy=False)
 
     if sort:
-        result = result.sort_values(ascending=ascending)
+        result = result.sort_values(ascending=ascending, kind="stable")
 
     if normalize:
         result = result / counts.sum()
diff --git a/pandas/core/base.py b/pandas/core/base.py
index b417cf1487417..200b16b4b6b1a 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -993,7 +993,12 @@ def value_counts(
             If True then the object returned will contain the relative
             frequencies of the unique values.
         sort : bool, default True
-            Sort by frequencies when True. Preserve the order of the data when False.
+            Stable sort by frequencies when True. Preserve the order of the data
+            when False.
+
+            .. versionchanged:: 3.0.0
+
+                Prior to 3.0.0, the sort was unstable.
         ascending : bool, default False
             Sort in ascending order.
         bins : int, optional
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 2b9adb6230028..60141548db9f0 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -7761,11 +7761,16 @@ def value_counts(
         normalize : bool, default False
             Return proportions rather than frequencies.
         sort : bool, default True
-            Sort by frequencies when True. Preserve the order of the data when False.
+            Stable sort by frequencies when True. Preserve the order of the data
+            when False.
 
             .. versionchanged:: 3.0.0
 
                 Prior to 3.0.0, ``sort=False`` would sort by the columns values.
+
+            .. versionchanged:: 3.0.0
+
+                Prior to 3.0.0, the sort was unstable.
         ascending : bool, default False
             Sort in ascending order.
         dropna : bool, default True
@@ -7875,7 +7880,7 @@ def value_counts(
         counts.name = name
 
         if sort:
-            counts = counts.sort_values(ascending=ascending)
+            counts = counts.sort_values(ascending=ascending, kind="stable")
         if normalize:
             counts /= counts.sum()
 
diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index 93e04fe61555e..dfa875249afff 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -2776,8 +2776,8 @@ def value_counts(
         normalize : bool, default False
             Return proportions rather than frequencies.
         sort : bool, default True
-            Sort by frequencies when True. When False, non-grouping columns will appear
-            in the order they occur in within groups.
+            Stable sort by frequencies when True. When False, non-grouping
+            columns will appear in the order they occur in within groups.
 
             .. versionchanged:: 3.0.0
 
diff --git a/pandas/tests/test_algos.py b/pandas/tests/test_algos.py
index c876aae6dea5e..588cd08a6b618 100644
--- a/pandas/tests/test_algos.py
+++ b/pandas/tests/test_algos.py
@@ -1446,6 +1446,19 @@ def test_value_counts_series(self):
         )
         tm.assert_series_equal(result, expected)
 
+    def test_value_counts_stability(self):
+        # GH 63155
+        arr = np.random.default_rng(2).integers(0, 32, 64)
+        result = algos.value_counts_internal(arr, sort=True)
+
+        value_counts = Series(arr).value_counts(sort=False)
+        expected = value_counts.sort_values(ascending=False, kind="stable")
+        tm.assert_series_equal(result, expected)
+
+        unstable_sorted = value_counts.sort_values(ascending=False, kind="quicksort")
+        with pytest.raises(AssertionError):
+            tm.assert_series_equal(result, unstable_sorted)
+
 
 class TestDuplicated:
     def test_duplicated_with_nas(self):