diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 24ff240cea3..c22b252728f 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -51,6 +51,9 @@ Bug fixes
 - Fixed labeled indexing with slice bounds given by xarray objects with
   datetime64 or timedelta64 dtypes (:issue:`1240`).
   By `Stephan Hoyer <https://github.com/shoyer>`_.
+- Attempting to convert an xarray.Dataset into a numpy array now raises an
+  informative error message.
+  By `Stephan Hoyer <https://github.com/shoyer>`_.
 - Fixed a bug in decode_cf_datetime where ``int32`` arrays weren't parsed
   correctly (:issue:`2002`).
   By `Fabien Maussion <https://github.com/fmaussion>`_.
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index e960d433f98..f28e7980b34 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -849,6 +849,12 @@ def __iter__(self):
                       FutureWarning, stacklevel=2)
         return iter(self._variables)
 
+    def __array__(self, dtype=None):
+        raise TypeError('cannot directly convert an xarray.Dataset into a '
+                        'numpy array. Instead, create an xarray.DataArray '
+                        'first, either with indexing on the Dataset or by '
+                        'invoking the `to_array()` method.')
+
     @property
     def nbytes(self):
         return sum(v.nbytes for v in self.variables.values())
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index b4ca14d2384..826f50003fa 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -443,6 +443,11 @@ def test_properties(self):
         assert Dataset({'x': np.int64(1),
                         'y': np.float32([1, 2])}).nbytes == 16
 
+    def test_asarray(self):
+        ds = Dataset({'x': 0})
+        with raises_regex(TypeError, 'cannot directly convert'):
+            np.asarray(ds)
+
     def test_get_index(self):
         ds = Dataset({'foo': (('x', 'y'), np.zeros((2, 3)))},
                      coords={'x': ['a', 'b']})