Vaughan sustained the broken nose just before half-time and received treatment.
Vaughan looks set to go into hospital on Monday to have surgery to reset it the broken nose.
Gradi told the official site "He has broken his nose and that usually takes at least four or five weeks to heal properly. It is a nuisance because I think David has added a real determination to his game over the last few matches. He was excellent the other night and played his part in what I thought was a magnificent team goal.
"Vaughan was going to be crucial for us and we were all set to do some work with him in and around the opposition's penalty area. We can't do that now and that is a blow because he has been playing well for us of late."
The player who had been linked with a few clubs over recent weeks looks set to have a spell on the sidelines and may miss out on any move during the transfer window.