diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index a5b7b36142e..8b145924f2d 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -56,6 +56,10 @@ Enhancements
 Bug fixes
 ~~~~~~~~~
 
+- ``xarray.DataArray.roll`` correctly handles multidimensional arrays.
+  (:issue:`2445`)
+  By `Keisuke Fujii <https://github.com/fujiisoup>`_.
+
 - ``xarray.DataArray.std()`` now correctly accepts ``ddof`` keyword argument.
   (:issue:`2240`)
   By `Keisuke Fujii <https://github.com/fujiisoup>`_.
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 4ad5902ebad..5e787c1587b 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -3595,7 +3595,8 @@ def roll(self, shifts=None, roll_coords=None, **shifts_kwargs):
         variables = OrderedDict()
         for k, v in iteritems(self.variables):
             if k not in unrolled_vars:
-                variables[k] = v.roll(**shifts)
+                variables[k] = v.roll(**{k: s for k, s in shifts.items()
+                                         if k in v.dims})
             else:
                 variables[k] = v
 
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index c42b84c05fc..2c964b81b98 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -3945,6 +3945,16 @@ def test_roll_coords_none(self):
         expected = Dataset({'foo': ('x', [3, 1, 2])}, ex_coords, attrs)
         assert_identical(expected, actual)
 
+    def test_roll_multidim(self):
+        # regression test for 2445
+        arr = xr.DataArray(
+            [[1, 2, 3],[4, 5, 6]], coords={'x': range(3), 'y': range(2)},
+            dims=('y','x'))
+        actual = arr.roll(x=1, roll_coords=True)
+        expected = xr.DataArray([[3, 1, 2],[6, 4, 5]],
+                                coords=[('y', [0, 1]), ('x', [2, 0, 1])])
+        assert_identical(expected, actual)
+
     def test_real_and_imag(self):
         attrs = {'foo': 'bar'}
         ds = Dataset({'x': ((), 1 + 2j, attrs)}, attrs=attrs)