diff --git a/CHANGES b/CHANGES
index 9c889420fd6..d8a0675836e 100644
--- a/CHANGES
+++ b/CHANGES
@@ -22,6 +22,8 @@ Incompatible changes
   ``<div>``
 * #8508: LaTeX: uplatex becomes a default setting of latex_engine for Japanese
   documents
+* #5977: py domain: ``:var:``, ``:cvar:`` and ``:ivar:`` fields do not create
+  cross-references
 
 Deprecated
 ----------
diff --git a/sphinx/domains/python.py b/sphinx/domains/python.py
index 000e2e8d34f..5afe2993a4f 100644
--- a/sphinx/domains/python.py
+++ b/sphinx/domains/python.py
@@ -354,7 +354,7 @@ class PyObject(ObjectDescription):
                             'keyword', 'kwarg', 'kwparam'),
                      typerolename='class', typenames=('paramtype', 'type'),
                      can_collapse=True),
-        PyTypedField('variable', label=_('Variables'), rolename='obj',
+        PyTypedField('variable', label=_('Variables'),
                      names=('var', 'ivar', 'cvar'),
                      typerolename='class', typenames=('vartype',),
                      can_collapse=True),
diff --git a/tests/test_domain_py.py b/tests/test_domain_py.py
index 14e9334486f..537bae15bb6 100644
--- a/tests/test_domain_py.py
+++ b/tests/test_domain_py.py
@@ -852,14 +852,12 @@ def test_info_field_list_var(app):
 
     # :var int attr:
     assert_node(doctree[1][1][0][0][1][0],
-                ([pending_xref, addnodes.literal_strong, "attr"],
+                ([addnodes.literal_strong, "attr"],
                  " (",
                  [pending_xref, addnodes.literal_emphasis, "int"],
                  ")",
                  " -- ",
                  "blah blah"))
-    assert_node(doctree[1][1][0][0][1][0][0], pending_xref,
-                refdomain="py", reftype="obj", reftarget="attr", **{"py:class": "Class"})
     assert_node(doctree[1][1][0][0][1][0][2], pending_xref,
                 refdomain="py", reftype="class", reftarget="int", **{"py:class": "Class"})