SOURCE

var Main = {
    data() {
        return {
            minDate: '',
            value7: ''
        }
    },
    computed: {
        pickerOptions() {
            let _this = this
            return {
                disabledDate(time) {
                    const times = 86400000 * 7//一周的毫秒数
                    let curSelectTime = new Date(_this.minDate).getTime()
                    let before = curSelectTime - times//前一周毫秒数
                    let after = curSelectTime + times//后一周毫秒数
                    return time.getTime() > after || time.getTime() < before
                },
                onPick({ maxDate, minDate }) {
                    if (!maxDate) {
                        _this.minDate = minDate
                    }
                }
            }
        }
    }
};
var Ctor = Vue.extend(Main)
new Ctor().$mount('#app')

<script src="//unpkg.com/vue/dist/vue.js"></script>
<script src="//unpkg.com/element-ui@2.6.0/lib/index.js"></script>
<div id="app">
  <template>
    <div class="block">
      <div>{{ value7 }}</div>
      <el-date-picker v-model="value7"
        ref="picker"
        type="daterange" 
        value-format="yyyy-MM-dd"
        unlink-panels 
        range-separator="至" 
        start-placeholder="开始日期" 
        end-placeholder="结束日期" 
        :picker-options="pickerOptions"
        @blur="minDate = ''">
      </el-date-picker>
    </div>
  </template>
</div>

@import url("//unpkg.com/element-ui@2.5.4/lib/theme-chalk/index.css");