Use <v-avatar inside a <v-btn icon> to create an avatar button:
<v-btn icon>
  <v-avatar>
    <img src="https://randomuser.me/api/portraits/men/1.jpg">
  </v-avatar>
</v-btn>          
Vuetify 0.14
The avatar's image should be the same size as that of the buttons.
The icon buttons are sized 36px by 36px, but the avatar image is sized 40px by 40px - so the avatar images appears too large when compared to other buttons (on the toolbar).
https://codepen.io/wernerm/pen/OjxpOK
_Please Note_ that the codepen's stylesheet contains styles to change the avatar image size.
As of 0.14.9 you can just assign the image size as the explicit height/width declaration of images inside of avatars was moved to only be within lists.
And it appears that change didn't make it in for latest release.
This should be fixed now, https://codepen.io/johnjleider/pen/veBWxJ
Check this example:
https://codepen.io/anon/pen/WMoybE
Overlay has wrong dimensions - to height and to narrow.
That is a completely separate problem. Please use the issue creator to create a new issue, do not comment on unrelated and closed issues.
I think you can use like this
<v-btn fab icon>
    <v-avatar
        size="45"
     >
         // image
     </v-avatar>
</v-btn>
fab and icon attributes in v-btn tag
You can also do this:
<v-btn icon width="auto" height="auto"  class="pa-1" style="border: 2px solid #a9dff1;">
        <v-avatar size="70">
         // image
        </v-avatar>
        </v-btn>
                    
Most helpful comment
I think you can use like this
fab and icon attributes in v-btn tag