The defender sustained the injury on his Blues debut against Cambridge United on Tuesday evening.
To make matters worse it happened after the former Dundee United player collided with his own goalkeeper Colin Doyle during the first-half of the Capital One Cup first round victory against the U's.
"Gavin has had a scan and it’s not very positive," said Clark.
"He’s done some damage to his posterior cruciate ligament, so we have to get that assessed by a surgeon but it’s not looking too good at the moment.
"I expect us to be without Gavin for a good period of time."