Update

Holy wow! I asked the Vuetify community to add documentation to their api, and it looks like they just added the to prop as well as other vue-router props to the Vuetify tabs docs. Seriously, the community there is awesome.

Original Answer

The folks in the Vuetify community Discord were able to help me out. My updated jsfiddle now has the working code.

Essentially, v-tab is a wrapper for router-link, where I assume it uses slots to pass props to router-link, so putting the to prop on v-tab works fine.

The following code is an example of the working code:

html

<v-app dark>
  <v-tabs fixed-tabs>
    <v-tab to="/foo">Foo</v-tab>
    <v-tab to="/bar">Bar</v-tab>
  </v-tabs>
  <router-view></router-view>
</v-app>

js

const Foo = {
  template: '<div>Foo component!</div>'
};

const Bar = {
  template: '<div>Bar component!</div>'
};

const routes = [
  { path: '/foo', component: Foo },
  { path: '/bar', component: Bar },
];

const router = new VueRouter({ routes });

new Vue({
  el: '#app',
  router,
});

Result

The template part:

<div>
    <v-tabs
      class="tabs"
      centered
      grow
      height="60px"
      v-model="activeTab"
    >
      <v-tab v-for="tab in tabs" :key="tab.id" :to="tab.route" exact>
        {{ tab.name }}
      </v-tab>
    </v-tabs>
    <router-view></router-view>
</div>

And the js part:

  data() {
    return {
      activeTab: `/user/${this.id}`,
      tabs: [
        { id: 1, name: "Task", route: `/user/${this.id}` },
        { id: 2, name: "Project", route: `/user/${this.id}/project` }
      ]
    };
  }

Routes:

{
  path: "/user/:id",
  component: User1,
  props: true,
  children: [
    {
      path: "", //selected tab by default
      component: TaskTab
    },
    {
      path: "project",
      component: ProjectTab
    }
  ]
}

See codesanbox example

I'm just adding some animation-related tips here & clarifying the use of v-tab-items vs v-tab-item.

If you have noticed, using the working markup as follows prevents the v-tabs tab switch animation to work:

<v-tabs v-model="activeTab">
  <v-tab key="tab-1" to="/tab-url-1">tab 1</v-tab>
  <v-tab key="tab-2" to="/tab-url-2">tab 2</v-tab>
</v-tabs>
<router-view />

If you want to keep the tab switch animation, this is a way to do it.

<v-tabs v-model="activeTab">
  <v-tab key="tab-1" to="/tab-url-1" ripple>
    tab 1
  </v-tab>
  <v-tab key="tab-2" to="/tab-url-2" ripple>
    tab 2
  </v-tab>

  <v-tab-item id="/tab-url-1">
    <router-view v-if="activeTab === '/tab-url-1'" />
  </v-tab-item>
  <v-tab-item id="/tab-url-2">
    <router-view v-if="activeTab === '/tab-url-2'" />
  </v-tab-item>
</v-tabs>

Note that you can also use a v-for loop on your v-tab and v-tab-item tags as long as your to value is found among the id attribute of your v-tab-items.

If you need to place your tab contents in a different place than your tabs buttons, this is what v-tab-items is for. You can place the v-tab-items in a v-tab-items tag outside of the v-tabs component. Make sure you give it a v-model="activeTab" attribute.