var endDate = new Date();
var numberOfDaysToAdd = 13;
endDate.setDate(endDate.getDate() + numberOfDaysToAdd);

var currDate = new Date();

<DatePicker
    dateFormat="YYYY-MM-DD"
    todayButton={"Today"}
    selected={this.state.startDate}
    onChange={this.handleChange}
    highlightDates = {[currDate,endDate]}
/>