diff --git a/rest_framework/renderers.py b/rest_framework/renderers.py
index ec6ac3dd8f..ad1adbaeaa 100644
--- a/rest_framework/renderers.py
+++ b/rest_framework/renderers.py
@@ -496,6 +496,17 @@ def get_rendered_html_form(self, data, view, method, request):
             existing_serializer = None
 
         with override_method(view, request, method) as request:
+            if method == 'OPTIONS':
+                # The browsable API only needs a placeholder for OPTIONS, so
+                # avoid object-level permission checks against serializer.instance.
+                if method not in view.allowed_methods:
+                    return
+                try:
+                    view.check_permissions(request)
+                except exceptions.APIException:
+                    return
+                return True
+
             if not self.show_form_for_method(view, method, request, instance):
                 return
 
diff --git a/tests/test_renderers.py b/tests/test_renderers.py
index 3e3e7512f4..3d5f6d758f 100644
--- a/tests/test_renderers.py
+++ b/tests/test_renderers.py
@@ -731,9 +731,34 @@ class AuthExampleViewSet(ExampleViewSet):
     class SimpleSerializer(serializers.Serializer):
         name = serializers.CharField()
 
+    class CrashOnObjectPermission(permissions.BasePermission):
+        def has_permission(self, request, view):
+            return True
+
+        def has_object_permission(self, request, view, obj):
+            return obj.user.is_staff
+
+    class Issue6855Serializer(serializers.Serializer):
+        name = serializers.CharField()
+
+    class Issue6855Object:
+        def __init__(self, name):
+            self.name = name
+
+    class Issue6855ViewSet(ViewSet):
+        @action(detail=True)
+        def extra_action(self, request, pk=None):
+            serializer = BrowsableAPIRendererTests.Issue6855Serializer(
+                BrowsableAPIRendererTests.Issue6855Object(name='demo')
+            )
+            return Response(serializer.data)
+
+    Issue6855ViewSet.permission_classes = [CrashOnObjectPermission]
+
     router = SimpleRouter()
     router.register('examples', ExampleViewSet, basename='example')
     router.register('auth-examples', AuthExampleViewSet, basename='auth-example')
+    router.register('issue-6855', Issue6855ViewSet, basename='issue-6855')
     urlpatterns = [path('api/', include(router.urls))]
 
     def setUp(self):
@@ -820,6 +845,34 @@ def test_extra_actions_dropdown_not_authed(self):
         assert '/api/examples/list_action/' not in resp.content.decode()
         assert '>Extra list action<' not in resp.content.decode()
 
+    def test_options_form_does_not_check_object_permissions_for_extra_action(self):
+        resp = self.client.get('/api/issue-6855/1/extra_action/', HTTP_ACCEPT='text/html')
+        assert resp.status_code == status.HTTP_200_OK
+
+    def test_delete_form_still_checks_object_permissions(self):
+        class ObjectPermissionDenied(permissions.BasePermission):
+            def has_permission(self, request, view):
+                return True
+
+            def has_object_permission(self, request, view, obj):
+                return False
+
+        class DummyObject:
+            name = 'Name'
+
+        class DummyDeleteView(APIView):
+            permission_classes = [ObjectPermissionDenied]
+
+            def delete(self, request):
+                return Response()
+
+        request = Request(APIRequestFactory().get('/'))
+        serializer = BrowsableAPIRendererTests.SimpleSerializer(instance=DummyObject())
+        delete_form = self.renderer.get_rendered_html_form(
+            serializer.data, DummyDeleteView(), 'DELETE', request
+        )
+        assert delete_form is None
+
 
 class AdminRendererTests(TestCase):