diff --git a/pandas/core/indexing.py b/pandas/core/indexing.py
index 9bfbc22b1e628..26aa5e3a71302 100644
--- a/pandas/core/indexing.py
+++ b/pandas/core/indexing.py
@@ -667,6 +667,9 @@ def _ensure_listlike_indexer(self, key, axis=None, value=None):
                 if k not in self.obj:
                     if value is None:
                         self.obj[k] = np.nan
+                    elif is_array_like(value) and value.ndim == 2:
+                        # GH#37964 have to select columnwise in case of array
+                        self.obj[k] = value[:, i]
                     elif is_list_like(value):
                         self.obj[k] = value[i]
                     else:
diff --git a/pandas/tests/frame/indexing/test_setitem.py b/pandas/tests/frame/indexing/test_setitem.py
index e4c57dc2b72fc..cd3102836422f 100644
--- a/pandas/tests/frame/indexing/test_setitem.py
+++ b/pandas/tests/frame/indexing/test_setitem.py
@@ -289,6 +289,21 @@ def test_setitem_periodindex(self):
         assert isinstance(rs.index, PeriodIndex)
         tm.assert_index_equal(rs.index, rng)
 
+    def test_setitem_complete_column_with_array(self):
+        # GH#37954
+        df = DataFrame({"a": ["one", "two", "three"], "b": [1, 2, 3]})
+        arr = np.array([[1, 1], [3, 1], [5, 1]])
+        df[["c", "d"]] = arr
+        expected = DataFrame(
+            {
+                "a": ["one", "two", "three"],
+                "b": [1, 2, 3],
+                "c": [1, 3, 5],
+                "d": [1, 1, 1],
+            }
+        )
+        tm.assert_frame_equal(df, expected)
+
 
 class TestDataFrameSetItemSlicing:
     def test_setitem_slice_position(self):