diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index c77348b365370..106c2579cd31a 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -441,6 +441,7 @@ Groupby/resample/rolling
 - Bug in :meth:`.Resampler.interpolate` on a :class:`DataFrame` with non-uniform sampling and/or indices not aligning with the resulting resampled index would result in wrong interpolation (:issue:`21351`)
 - Bug in :meth:`DataFrame.ewm` and :meth:`Series.ewm` when passed ``times`` and aggregation functions other than mean (:issue:`51695`)
 - Bug in :meth:`DataFrameGroupBy.apply` that was returning a completely empty DataFrame when all return values of ``func`` were ``None`` instead of returning an empty DataFrame with the original columns and dtypes. (:issue:`57775`)
+- Bug in :meth:`DataFrameGroupBy.apply` with ``as_index=False`` that was returning :class:`MultiIndex` instead of returning :class:`Index`. (:issue:`58291`)
 
 
 Reshaping
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index 79d9f49a3b355..f44ef8c4dbbfa 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -1202,10 +1202,7 @@ def _concat_objects(
                     sort=False,
                 )
             else:
-                # GH5610, returns a MI, with the first level being a
-                # range index
-                keys = RangeIndex(len(values))
-                result = concat(values, axis=0, keys=keys)
+                result = concat(values, axis=0)
 
         elif not not_indexed_same:
             result = concat(values, axis=0)
diff --git a/pandas/tests/groupby/methods/test_value_counts.py b/pandas/tests/groupby/methods/test_value_counts.py
index be52b4a591c26..0f136b06c782a 100644
--- a/pandas/tests/groupby/methods/test_value_counts.py
+++ b/pandas/tests/groupby/methods/test_value_counts.py
@@ -329,13 +329,10 @@ def test_against_frame_and_seriesgroupby(
         else:
             name = "proportion" if normalize else "count"
             expected = expected.reset_index().rename({0: name}, axis=1)
-            if groupby == "column":
-                expected = expected.rename({"level_0": "country"}, axis=1)
-                expected["country"] = np.where(expected["country"], "US", "FR")
-            elif groupby == "function":
-                expected["level_0"] = expected["level_0"] == 1
+            if groupby in ["array", "function"] and (not as_index and frame):
+                expected.insert(loc=0, column="level_0", value=result["level_0"])
             else:
-                expected["level_0"] = np.where(expected["level_0"], "US", "FR")
+                expected.insert(loc=0, column="country", value=result["country"])
             tm.assert_frame_equal(result, expected)
     else:
         # compare against SeriesGroupBy value_counts
diff --git a/pandas/tests/groupby/test_apply.py b/pandas/tests/groupby/test_apply.py
index 1a2589fe94ea5..e27c782c1bdcf 100644
--- a/pandas/tests/groupby/test_apply.py
+++ b/pandas/tests/groupby/test_apply.py
@@ -315,7 +315,7 @@ def test_groupby_as_index_apply():
 
     # apply doesn't maintain the original ordering
     # changed in GH5610 as the as_index=False returns a MI here
-    exp_not_as_apply = MultiIndex.from_tuples([(0, 0), (0, 2), (1, 1), (2, 4)])
+    exp_not_as_apply = Index([0, 2, 1, 4])
     tp = [(1, 0), (1, 2), (2, 1), (3, 4)]
     exp_as_apply = MultiIndex.from_tuples(tp, names=["user_id", None])
 
diff --git a/pandas/tests/groupby/test_apply_mutate.py b/pandas/tests/groupby/test_apply_mutate.py
index e5028884e992b..fa20efad4da77 100644
--- a/pandas/tests/groupby/test_apply_mutate.py
+++ b/pandas/tests/groupby/test_apply_mutate.py
@@ -90,9 +90,7 @@ def fn(x):
         result = df.groupby(["col1"], as_index=False).apply(fn)
     expected = pd.Series(
         [1, 2, 0, 4, 5, 0],
-        index=pd.MultiIndex.from_tuples(
-            [(0, 0), (0, 1), (0, 2), (1, 3), (1, 4), (1, 5)]
-        ),
+        index=range(6),
         name="col2",
     )
     tm.assert_series_equal(result, expected)
diff --git a/pandas/tests/groupby/test_groupby.py b/pandas/tests/groupby/test_groupby.py
index 54d7895691f3f..d50fea459552a 100644
--- a/pandas/tests/groupby/test_groupby.py
+++ b/pandas/tests/groupby/test_groupby.py
@@ -113,8 +113,9 @@ def f(x, q=None, axis=0):
         expected_seq = df_grouped.quantile([0.4, 0.8])
         if not as_index:
             # apply treats the op as a transform; .quantile knows it's a reduction
-            apply_result = apply_result.reset_index()
-            apply_result["level_0"] = [1, 1, 2, 2]
+            apply_result.index = range(4)
+            apply_result.insert(loc=0, column="level_0", value=[1, 1, 2, 2])
+            apply_result.insert(loc=1, column="level_1", value=[0.4, 0.8, 0.4, 0.8])
         tm.assert_frame_equal(apply_result, expected_seq, check_names=False)
 
         agg_result = df_grouped.agg(f, q=80)
@@ -519,9 +520,7 @@ def test_as_index_select_column():
     result = df.groupby("A", as_index=False, group_keys=True)["B"].apply(
         lambda x: x.cumsum()
     )
-    expected = Series(
-        [2, 6, 6], name="B", index=MultiIndex.from_tuples([(0, 0), (0, 1), (1, 2)])
-    )
+    expected = Series([2, 6, 6], name="B", index=range(3))
     tm.assert_series_equal(result, expected)