jsfiddle
var dateControl = document.querySelector('input[type="date"]');
dateControl.value = '2017-06-01';
<div style="width:100%;"> <form name='przypomnienie' method='GET' action='zapiszpprzypomnienie.php'> <div class="form-group"> <table border="0" class="table table-hover"> <thead> <tr> <td align='center'>id</td> <td align='center'>kategoria</td> <td align='center'>data</td> </tr> </thead> <tbody> <tr> <td align='center'><input type='text' class='form-control' name='id' value='<?php echo $id; ?>' size='3'></td> <td align='center'><input type='text' class='form-control' name='kategoria' value='' size='20' autofocus></td> <td align='center'><input type='date' class='form-control' name='data' value='<?php echo $dzisiaj; ?>' size='15'></td> </tr> </tbody> </table> >>> 7 dni <br/> <button type='submit' class='btn btn-primary'>zapisz</button> </form> </div>