In version 1.6, there is no direct callback method to do it. If you are using fullcalendar.min.js, you can do it by creating a function like :-
function yourfunction(currentDate)
{
// your code
}
and place it above the
<script src="/fullcalendar/fullcalendar/fullcalendar.min.js" type="text/javascript"></script>
Then find the code "l(){var t,e,n,r,a=f(new Date);" in fullcalendar.min.js and call your function before closing tag of function "l". Your code will look like this :-
l(){var t,e,n,r,a=f(new Date);if(Qe){var o=un(N(0),Ke);Je?o+=Ge:o=Ge+o,ee.find(".fc-week-number").text(o)}for(t=0;Le>t;t++)r=N(t),e=ne.eq(t),e.html(un(r,$e)),n=ae.eq(t),+r==+a?n.addClass(Ye+"-state-highlight fc-today"):n.removeClass(Ye+"-state-highlight fc-today"),yourfunction(r)==false?n.addClass("fc-disabled"):n.removeClass('fc-disabled'),$(e.add(n),r)}
I am adding class to disable the day. Good luck..!!