diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 42da3fa8e63..eeb768224e6 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -18,6 +18,14 @@ What's New
 v0.13.1 (unreleased)
 --------------------
 
+Bug fixes
+~~~~~~~~~
+- Reintroduce support for :mod:`weakref` (broken in v0.13.0). Support has been
+  reinstated for :class:`DataArray` and :class:`Dataset` objects only. Internal xarray
+  objects remain unaddressable by weakref in order to save memory.
+  (:issue:`3317`) by `Guido Imperiale <https://github.com/crusaderky>`_.
+
+
 .. _whats-new.0.13.0:
 
 v0.13.0 (17 Sep 2019)
diff --git a/xarray/core/dataarray.py b/xarray/core/dataarray.py
index d9e98839419..13a3a507c7b 100644
--- a/xarray/core/dataarray.py
+++ b/xarray/core/dataarray.py
@@ -248,7 +248,15 @@ class DataArray(AbstractArray, DataWithCoords):
         Dictionary for holding arbitrary metadata.
     """
 
-    __slots__ = ("_accessors", "_coords", "_file_obj", "_name", "_indexes", "_variable")
+    __slots__ = (
+        "_accessors",
+        "_coords",
+        "_file_obj",
+        "_name",
+        "_indexes",
+        "_variable",
+        "__weakref__",
+    )
 
     _groupby_cls = groupby.DataArrayGroupBy
     _rolling_cls = rolling.DataArrayRolling
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 693e94e22dd..3ba1bd9e3d8 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -420,6 +420,7 @@ class Dataset(Mapping, ImplementsDatasetReduce, DataWithCoords):
         "_file_obj",
         "_indexes",
         "_variables",
+        "__weakref__",
     )
 
     _groupby_cls = groupby.DatasetGroupBy
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index 01e92bdd7be..9ba3eecc5a0 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -4672,3 +4672,14 @@ class MyArray(DataArray):
             pass
 
     assert str(e.value) == "MyArray must explicitly define __slots__"
+
+
+def test_weakref():
+    """Classes with __slots__ are incompatible with the weakref module unless they
+    explicitly state __weakref__ among their slots
+    """
+    from weakref import ref
+
+    a = DataArray(1)
+    r = ref(a)
+    assert r() is a
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 7d2b11d02c9..f02990a1be9 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -5786,3 +5786,14 @@ class MyDS(Dataset):
             pass
 
     assert str(e.value) == "MyDS must explicitly define __slots__"
+
+
+def test_weakref():
+    """Classes with __slots__ are incompatible with the weakref module unless they
+    explicitly state __weakref__ among their slots
+    """
+    from weakref import ref
+
+    ds = Dataset()
+    r = ref(ds)
+    assert r() is ds