diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index 759c7fb65374d..4c6a32ff1ba4e 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -2291,18 +2291,28 @@ def _concat_same_type(
     ) -> CategoricalT:
         from pandas.core.dtypes.concat import union_categoricals
 
-        result = union_categoricals(to_concat)
-
-        # in case we are concatenating along axis != 0, we need to reshape
-        #  the result from union_categoricals
         first = to_concat[0]
         if axis >= first.ndim:
-            raise ValueError
+            raise ValueError(
+                f"axis {axis} is out of bounds for array of dimension {first.ndim}"
+            )
+
         if axis == 1:
-            if not all(len(x) == len(first) for x in to_concat):
+            # Flatten, concatenate then reshape
+            if not all(x.ndim == 2 for x in to_concat):
                 raise ValueError
-            # TODO: Will this get contiguity wrong?
-            result = result.reshape(-1, len(to_concat), order="F")
+
+            # pass correctly-shaped to union_categoricals
+            tc_flat = []
+            for obj in to_concat:
+                tc_flat.extend([obj[:, i] for i in range(obj.shape[1])])
+
+            res_flat = cls._concat_same_type(tc_flat, axis=0)
+
+            result = res_flat.reshape(len(first), -1, order="F")
+            return result
+
+        result = union_categoricals(to_concat)
         return result
 
     # ------------------------------------------------------------------
diff --git a/pandas/core/dtypes/concat.py b/pandas/core/dtypes/concat.py
index 28f415476d3fd..701f9fd4a9c99 100644
--- a/pandas/core/dtypes/concat.py
+++ b/pandas/core/dtypes/concat.py
@@ -107,7 +107,9 @@ def is_nonempty(x) -> bool:
         to_concat = non_empties
 
     kinds = {obj.dtype.kind for obj in to_concat}
-    contains_datetime = any(kind in ["m", "M"] for kind in kinds)
+    contains_datetime = any(kind in ["m", "M"] for kind in kinds) or any(
+        isinstance(obj, ABCExtensionArray) and obj.ndim > 1 for obj in to_concat
+    )
 
     all_empty = not len(non_empties)
     single_dtype = len({x.dtype for x in to_concat}) == 1
diff --git a/pandas/tests/dtypes/test_concat.py b/pandas/tests/dtypes/test_concat.py
index a749955d35494..f624c56b54001 100644
--- a/pandas/tests/dtypes/test_concat.py
+++ b/pandas/tests/dtypes/test_concat.py
@@ -26,3 +26,21 @@ def test_concat_single_dataframe_tz_aware(copy):
     expected = df.copy()
     result = pd.concat([df], copy=copy)
     tm.assert_frame_equal(result, expected)
+
+
+def test_concat_periodarray_2d():
+    pi = pd.period_range("2016-01-01", periods=36, freq="D")
+    arr = pi._data.reshape(6, 6)
+
+    result = _concat.concat_compat([arr[:2], arr[2:]], axis=0)
+    tm.assert_period_array_equal(result, arr)
+
+    result = _concat.concat_compat([arr[:, :2], arr[:, 2:]], axis=1)
+    tm.assert_period_array_equal(result, arr)
+
+    msg = "all the input array dimensions for the concatenation axis must match exactly"
+    with pytest.raises(ValueError, match=msg):
+        _concat.concat_compat([arr[:, :2], arr[:, 2:]], axis=0)
+
+    with pytest.raises(ValueError, match=msg):
+        _concat.concat_compat([arr[:2], arr[2:]], axis=1)
diff --git a/pandas/tests/extension/base/dim2.py b/pandas/tests/extension/base/dim2.py
index 9328ddc91f10f..a86c07c604320 100644
--- a/pandas/tests/extension/base/dim2.py
+++ b/pandas/tests/extension/base/dim2.py
@@ -122,21 +122,23 @@ def test_tolist_2d(self, data):
         assert result == expected
 
     def test_concat_2d(self, data):
-        left = data.reshape(-1, 1)
+        left = type(data)._concat_same_type([data, data]).reshape(-1, 2)
         right = left.copy()
 
         # axis=0
         result = left._concat_same_type([left, right], axis=0)
-        expected = data._concat_same_type([data, data]).reshape(-1, 1)
+        expected = data._concat_same_type([data] * 4).reshape(-1, 2)
         self.assert_extension_array_equal(result, expected)
 
         # axis=1
         result = left._concat_same_type([left, right], axis=1)
-        expected = data.repeat(2).reshape(-1, 2)
-        self.assert_extension_array_equal(result, expected)
+        assert result.shape == (len(data), 4)
+        self.assert_extension_array_equal(result[:, :2], left)
+        self.assert_extension_array_equal(result[:, 2:], right)
 
         # axis > 1 -> invalid
-        with pytest.raises(ValueError):
+        msg = "axis 2 is out of bounds for array of dimension 2"
+        with pytest.raises(ValueError, match=msg):
             left._concat_same_type([left, right], axis=2)
 
     @pytest.mark.parametrize("method", ["backfill", "pad"])