diff --git a/rest_framework/schemas/inspectors.py b/rest_framework/schemas/inspectors.py
index e027b46a70..56a857394e 100644
--- a/rest_framework/schemas/inspectors.py
+++ b/rest_framework/schemas/inspectors.py
@@ -3,6 +3,7 @@
 
 See schemas.__init__.py for package overview.
 """
+import copy
 import re
 from weakref import WeakKeyDictionary
 
@@ -48,9 +49,15 @@ def __get__(self, instance, owner):
         return self
 
     def __set__(self, instance, other):
-        self.instance_schemas[instance] = other
         if other is not None:
+            # A single `ViewInspector` instance may be shared by multiple
+            # views, e.g. when `@action(schema=AutoSchema())` is used on a
+            # method defined in a mixin and reused across several ViewSets.
+            # Store an independent copy per view so that `other.view` isn't
+            # silently overwritten by whichever view is set last.
+            other = copy.copy(other)
             other.view = instance
+        self.instance_schemas[instance] = other
 
     @property
     def view(self):
diff --git a/tests/schemas/test_view_inspector.py b/tests/schemas/test_view_inspector.py
new file mode 100644
index 0000000000..7ef0cf42de
--- /dev/null
+++ b/tests/schemas/test_view_inspector.py
@@ -0,0 +1,52 @@
+import pytest
+from django.test import TestCase
+
+from rest_framework.compat import uritemplate
+from rest_framework.decorators import action
+from rest_framework.response import Response
+from rest_framework.routers import DefaultRouter
+from rest_framework.schemas.openapi import AutoSchema, SchemaGenerator
+from rest_framework.serializers import Serializer
+from rest_framework.viewsets import GenericViewSet
+
+
+class TestViewInspectorDescriptor(TestCase):
+    """
+    Regression tests for #6877: a `ViewInspector` (e.g. `AutoSchema`)
+    instance shared across multiple views, such as one assigned via
+    `@action(schema=AutoSchema())` on a method defined in a mixin, must
+    not leak the `view` it was last accessed with onto other views.
+    """
+    @pytest.mark.skipif(uritemplate is None, reason='uritemplate not installed.')
+    def test_schema_shared_via_mixin_action_is_not_shared_between_viewsets(self):
+        shared_schema = AutoSchema()
+
+        class CancelViewSetMixin:
+            @action(methods=['post'], detail=True, schema=shared_schema)
+            def cancel(self, request, pk):
+                return Response()
+
+        class ASerializer(Serializer):
+            pass
+
+        class BSerializer(Serializer):
+            pass
+
+        class ViewSetA(CancelViewSetMixin, GenericViewSet):
+            serializer_class = ASerializer
+
+        class ViewSetB(CancelViewSetMixin, GenericViewSet):
+            serializer_class = BSerializer
+
+        router = DefaultRouter()
+        router.register(r'view-set-a', ViewSetA, basename='viewseta')
+        router.register(r'view-set-b', ViewSetB, basename='viewsetb')
+
+        generator = SchemaGenerator(title='Test', patterns=router.urls)
+        schema = generator.get_schema(request=None, public=True)
+
+        operation_id_a = schema['paths']['/view-set-a/{id}/cancel/']['post']['operationId']
+        operation_id_b = schema['paths']['/view-set-b/{id}/cancel/']['post']['operationId']
+
+        assert operation_id_a == 'cancelA'
+        assert operation_id_b == 'cancelB'