How to disable value on the select option ? (vue.js 2)

You should add option directly in select tag.

<select class="form-control" v-model="selected" required>
  <option value="" disabled>Select a category</option>
  <option v-for="option in options" v-bind:value="option.id">{{ option.name }}</option>
</select>

Also, remove it from data function.

data() {
  return {
    selected: '',
    options: []
  };
}

I don't recommend you to add this option in the options array, because it is a placeholder attribute for your select.

Other option could be to disable that element using a binding

<option v-for="option in options" 
        :disabled="!option.id"
        v-bind:value="option.id">
    {{ option.name }}
</option>