diff --git a/sphinx/ext/graphviz.py b/sphinx/ext/graphviz.py
index bc348f4e1..f0b321378 100644
--- a/sphinx/ext/graphviz.py
+++ b/sphinx/ext/graphviz.py
@@ -290,21 +290,25 @@ def render_dot_html(self, node, code, options, prefix='graphviz',
             self.body.append('<div align="%s" class="align-%s">' %
                              (node['align'], node['align']))
         if format == 'svg':
-            svgtag = '''<object data="%s" type="image/svg+xml">
-            <p class="warning">%s</p></object>\n''' % (fname, alt)
+            svgtag = '''<div class="graphviz"><object data="%s" type="image/svg+xml">
+            <p class="warning">%s</p></object></div>\n''' % (fname, alt)
             self.body.append(svgtag)
         else:
             with codecs.open(outfn + '.map', 'r', encoding='utf-8') as mapfile:  # type: ignore
                 imgmap = ClickableMapDefinition(outfn + '.map', mapfile.read(), dot=code)
                 if imgmap.clickable:
                     # has a map
-                    self.body.append('<img src="%s" alt="%s" usemap="#%s" %s/>\n' %
+                    self.body.append('<div class="graphviz">')
+                    self.body.append('<img src="%s" alt="%s" usemap="#%s" %s/>' %
                                      (fname, alt, imgmap.id, imgcss))
+                    self.body.append('</div>\n')
                     self.body.append(imgmap.generate_clickable_map())
                 else:
                     # nothing in image map
-                    self.body.append('<img src="%s" alt="%s" %s/>\n' %
+                    self.body.append('<div class="graphviz">')
+                    self.body.append('<img src="%s" alt="%s" %s/>' %
                                      (fname, alt, imgcss))
+                    self.body.append('</div>\n')
         if 'align' in node:
             self.body.append('</div>\n')
 
diff --git a/tests/test_ext_graphviz.py b/tests/test_ext_graphviz.py
index 3efab6b56..df096ce62 100644
--- a/tests/test_ext_graphviz.py
+++ b/tests/test_ext_graphviz.py
@@ -22,24 +22,26 @@ def test_graphviz_png_html(app, status, warning):
     app.builder.build_all()
 
     content = (app.outdir / 'index.html').text()
-    html = (r'<div class="figure" .*?>\s*<img .*?/>\s*<p class="caption">'
+    html = (r'<div class="figure" .*?>\s*'
+            r'<div class="graphviz"><img .*?/></div>\s*<p class="caption">'
             r'<span class="caption-text">caption of graph</span>.*</p>\s*</div>')
     assert re.search(html, content, re.S)
 
-    html = 'Hello <img .*?/>\n graphviz world'
+    html = 'Hello <div class="graphviz"><img .*?/></div>\n graphviz world'
     assert re.search(html, content, re.S)
 
     html = '<img src=".*?" alt="digraph {\n  bar -&gt; baz\n}" />'
     assert re.search(html, content, re.M)
 
-    html = (r'<div class="figure align-right" .*?>\s*<img .*?/>\s*<p class="caption">'
+    html = (r'<div class="figure align-right" .*?>\s*'
+            r'<div class="graphviz"><img .*?/></div>\s*<p class="caption">'
             r'<span class="caption-text">on right</span>.*</p>\s*</div>')
     assert re.search(html, content, re.S)
 
     html = (r'<div align=\"center\" class=\"align-center\">'
-            r'<img src=\".*\.png\" alt=\"digraph foo {\n'
+            r'<div class="graphviz"><img src=\".*\.png\" alt=\"digraph foo {\n'
             r'centered\n'
-            r'}\" />\n</div>')
+            r'}\" /></div>\n</div>')
     assert re.search(html, content, re.S)
 
 
@@ -52,34 +54,34 @@ def test_graphviz_svg_html(app, status, warning):
     content = (app.outdir / 'index.html').text()
 
     html = (r'<div class=\"figure\" .*?>\n'
-            r'<object data=\".*\.svg\".*>\n'
+            r'<div class="graphviz"><object data=\".*\.svg\".*>\n'
             r'\s+<p class=\"warning\">digraph foo {\n'
             r'bar -&gt; baz\n'
-            r'}</p></object>\n'
+            r'}</p></object></div>\n'
             r'<p class=\"caption\"><span class=\"caption-text\">'
             r'caption of graph</span>.*</p>\n</div>')
     assert re.search(html, content, re.S)
 
-    html = (r'Hello <object.*>\n'
-            r'\s+<p class=\"warning\">graph</p></object>\n'
+    html = (r'Hello <div class="graphviz"><object.*>\n'
+            r'\s+<p class=\"warning\">graph</p></object></div>\n'
             r' graphviz world')
     assert re.search(html, content, re.S)
 
     html = (r'<div class=\"figure align-right\" .*\>\n'
-            r'<object data=\".*\.svg\".*>\n'
+            r'<div class="graphviz"><object data=\".*\.svg\".*>\n'
             r'\s+<p class=\"warning\">digraph bar {\n'
             r'foo -&gt; bar\n'
-            r'}</p></object>\n'
+            r'}</p></object></div>\n'
             r'<p class=\"caption\"><span class=\"caption-text\">'
             r'on right</span>.*</p>\n'
             r'</div>')
     assert re.search(html, content, re.S)
 
     html = (r'<div align=\"center\" class=\"align-center\">'
-            r'<object data=\".*\.svg\".*>\n'
+            r'<div class="graphviz"><object data=\".*\.svg\".*>\n'
             r'\s+<p class=\"warning\">digraph foo {\n'
             r'centered\n'
-            r'}</p></object>\n'
+            r'}</p></object></div>\n'
             r'</div>')
     assert re.search(html, content, re.S)
 
diff --git a/tests/test_ext_inheritance_diagram.py b/tests/test_ext_inheritance_diagram.py
index ad106e6c6..dfee015e0 100644
--- a/tests/test_ext_inheritance_diagram.py
+++ b/tests/test_ext_inheritance_diagram.py
@@ -25,8 +25,9 @@ def test_inheritance_diagram_html(app, status, warning):
     content = (app.outdir / 'index.html').text()
 
     pattern = ('<div class="figure" id="id1">\n'
+               '<div class="graphviz">'
                '<img src="_images/inheritance-\\w+.png" alt="Inheritance diagram of test.Foo" '
-               'class="inheritance"/>\n<p class="caption"><span class="caption-text">'
+               'class="inheritance"/></div>\n<p class="caption"><span class="caption-text">'
                'Test Foo!</span><a class="headerlink" href="#id1" '
                'title="Permalink to this image">\xb6</a></p>')
     assert re.search(pattern, content, re.M)
@@ -62,8 +63,9 @@ def test_inheritance_diagram_latex_alias(app, status, warning):
     content = (app.outdir / 'index.html').text()
 
     pattern = ('<div class="figure" id="id1">\n'
+               '<div class="graphviz">'
                '<img src="_images/inheritance-\\w+.png" alt="Inheritance diagram of test.Foo" '
-               'class="inheritance"/>\n<p class="caption"><span class="caption-text">'
+               'class="inheritance"/></div>\n<p class="caption"><span class="caption-text">'
                'Test Foo!</span><a class="headerlink" href="#id1" '
                'title="Permalink to this image">\xb6</a></p>')
     assert re.search(pattern, content, re.M)