diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 84ac2d0c17676..5c7ccd256a84c 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -769,6 +769,7 @@ Groupby/resample/rolling
 - Bug in :meth:`DataFrame.groupby` dropped ``nan`` groups from result with ``dropna=False`` when grouping over a single column (:issue:`35646`, :issue:`35542`)
 - Bug in :meth:`.DataFrameGroupBy.head`, :meth:`.DataFrameGroupBy.tail`, :meth:`SeriesGroupBy.head`, and :meth:`SeriesGroupBy.tail` would raise when used with ``axis=1`` (:issue:`9772`)
 - Bug in :meth:`.DataFrameGroupBy.transform` would raise when used with ``axis=1`` and a transformation kernel (e.g. "shift") (:issue:`36308`)
+- Bug in :meth:`.DataFrameGroupBy.quantile` couldn't handle with arraylike ``q`` when grouping by columns (:issue:`33795`)
 - Bug in :meth:`DataFrameGroupBy.rank` with ``datetime64tz`` or period dtype incorrectly casting results to those dtypes instead of returning ``float64`` dtype (:issue:`38187`)
 
 Reshaping
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index 184fa3a2b4204..ba4d7dd063c38 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -2232,29 +2232,36 @@ def post_processor(vals: np.ndarray, inference: Optional[Type]) -> np.ndarray:
                 )
                 for qi in q
             ]
-            result = concat(results, axis=0, keys=q)
+            result = concat(results, axis=self.axis, keys=q)
             # fix levels to place quantiles on the inside
             # TODO(GH-10710): Ideally, we could write this as
             #  >>> result.stack(0).loc[pd.IndexSlice[:, ..., q], :]
             #  but this hits https://github.com/pandas-dev/pandas/issues/10710
             #  which doesn't reorder the list-like `q` on the inner level.
-            order = list(range(1, result.index.nlevels)) + [0]
+            order = list(range(1, result.axes[self.axis].nlevels)) + [0]
 
             # temporarily saves the index names
-            index_names = np.array(result.index.names)
+            index_names = np.array(result.axes[self.axis].names)
 
             # set index names to positions to avoid confusion
-            result.index.names = np.arange(len(index_names))
+            result.axes[self.axis].names = np.arange(len(index_names))
 
             # place quantiles on the inside
-            result = result.reorder_levels(order)
+            if isinstance(result, Series):
+                result = result.reorder_levels(order)
+            else:
+                result = result.reorder_levels(order, axis=self.axis)
 
             # restore the index names in order
-            result.index.names = index_names[order]
+            result.axes[self.axis].names = index_names[order]
 
             # reorder rows to keep things sorted
-            indices = np.arange(len(result)).reshape([len(q), self.ngroups]).T.flatten()
-            return result.take(indices)
+            indices = (
+                np.arange(result.shape[self.axis])
+                .reshape([len(q), self.ngroups])
+                .T.flatten()
+            )
+            return result.take(indices, axis=self.axis)
 
     @Substitution(name="groupby")
     def ngroup(self, ascending: bool = True):
diff --git a/pandas/tests/groupby/test_quantile.py b/pandas/tests/groupby/test_quantile.py
index 53729a120ae8d..76fc82c6288eb 100644
--- a/pandas/tests/groupby/test_quantile.py
+++ b/pandas/tests/groupby/test_quantile.py
@@ -254,3 +254,26 @@ def test_groupby_timedelta_quantile():
         index=Index([1, 2], name="group"),
     )
     tm.assert_frame_equal(result, expected)
+
+
+def test_columns_groupby_quantile():
+    # GH 33795
+    df = DataFrame(
+        np.arange(12).reshape(3, -1),
+        index=list("XYZ"),
+        columns=pd.Series(list("ABAB"), name="col"),
+    )
+    result = df.groupby("col", axis=1).quantile(q=[0.8, 0.2])
+    expected = DataFrame(
+        [
+            [1.6, 0.4, 2.6, 1.4],
+            [5.6, 4.4, 6.6, 5.4],
+            [9.6, 8.4, 10.6, 9.4],
+        ],
+        index=list("XYZ"),
+        columns=Index(
+            [("A", 0.8), ("A", 0.2), ("B", 0.8), ("B", 0.2)], names=["col", None]
+        ),
+    )
+
+    tm.assert_frame_equal(result, expected)