Following code will set minDate as First date of current month and maxdate as last date of current month.
var currentTime = new Date();
var startDateFrom = new Date(currentTime.getFullYear(),currentTime.getMonth(),1);
var startDateTo = new Date(currentTime.getFullYear(),currentTime.getMonth() +1,0);
$("#datepicker").datepicker({
dateFormat: 'dd.mm.yy',
minDate: startDateFrom,
maxDate: startDateTo
});