diff --git a/docs/topics/search/backends.rst b/docs/topics/search/backends.rst
index 92134482f..3012900ef 100644
--- a/docs/topics/search/backends.rst
+++ b/docs/topics/search/backends.rst
@@ -115,7 +115,11 @@ Prerequisites are the `Elasticsearch`_ service itself and, via pip, the `elastic
 
 .. code-block:: sh
 
-  pip install "elasticsearch>=6.0.0,<7.0.0"  # for Elasticsearch 6.x
+  pip install "elasticsearch>=6.0.0,<6.3.1"  # for Elasticsearch 6.x
+
+.. warning::
+
+    | Version 6.3.1 of the Elasticsearch client library is incompatible with Wagtail. Use 6.3.0 or earlier.
 
 The backend is configured in settings:
 
diff --git a/tox.ini b/tox.ini
index 8131d5dd8..804382f67 100644
--- a/tox.ini
+++ b/tox.ini
@@ -48,7 +48,7 @@ deps =
     elasticsearch2: elasticsearch>=2,<3
     elasticsearch5: elasticsearch>=5,<6
     elasticsearch5: certifi
-    elasticsearch6: elasticsearch>=6,<7
+    elasticsearch6: elasticsearch>=6,<6.3.1
     elasticsearch6: certifi
 
 setenv =