JSFiddle - React, Tailwind, and code Playground

HTML

<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.1/jquery.js"></script>
<script src="http://ajax.googleapis.com/ajax/libs/jqueryui/1.7.2/jquery-ui.min.js"></script>
<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.7.2/themes/base/jquery-ui.css">
    <label for="startDate">Date :</label>
    <input name="startDate" id="startDate" class="date-picker" />

CSS

.ui-datepicker-calendar {
    display: none;
    }

JavaScript

$(function() {
        $('.date-picker').datepicker(
            {
                dateFormat: "yy-mm",
                changeMonth: true,
                changeYear: true,
                showButtonPanel: true,
                onClose: function(dateText, inst) {


                    function isDonePressed(){
                        return ($('#ui-datepicker-div').html().indexOf('ui-datepicker-close ui-state-default ui-priority-primary ui-corner-all ui-state-hover') > -1);
                    }

                    if (isDonePressed()){
                        var month = $("#ui-datepicker-div .ui-datepicker-month :selected").val();
                        var year = $("#ui-datepicker-div .ui-datepicker-year :selected").val();
                        $(this).datepicker('setDate', new Date(year, month, 1)).trigger('change');

                        $('.date-picker').focusout();//Added to remove focus from datepicker input box on selecting date
                    }
                },
                beforeShow : function(input, inst) {

                    inst.dpDiv.addClass('month_year_datepicker');


                    if ((datestr = $(this).val()).length > 0) {
                        year = datestr.substring(0, 4);
                        month = datestr.substring(datestr.length-2, datestr.length);

                        $(this).datepicker('option', 'defaultDate', new Date(year, month-1, 1));
                        $(this).datepicker('setDate', new Date(year, month-1, 1));
                        $(".ui-datepicker-calendar").hide();
                    }
                }
            }).datepicker("option", "defaultDate", new Date(2000, 6, 17)).datepicker('setDate', new Date(2000, 6, 17));
    });