Boss Aidy Boothroyd admits he may now be forced into the loan market for defensive cover.
"David is going to be out for 10 to 12 weeks," Boothroyd told the club's official website. "It's only a slight tear but if he were to keep playing with it then we'd have a major problem.
"We've pulled him right out of everything and now he's got to have a period of rest and rehabilitation. It is a blow but these things do happen and we just have to deal with it and get on with it.
"Anthony Charles came back in on Saturday and I thought he did very well so we've just got to try and maintain what we've been doing.
"We have been a bit unfortunate with injuries but I'm hoping it will even itself out and I'd rather have these injuries now than in the latter part of the season. We might have to look at bringing in another defender but we are just going to take it game by game for the time being."