The 29-year-old Scot, who has made 18 appearances for the Dons this season, suffered the injury in training late last week.
Manager Neal Ardley admits the setback could force him into the loan market to find a replacement.
"Peter could be out for six to eight weeks," said Ardley.
"It's a big blow and I really feel for Peter because he has been playing really well. We will have to look at that area because now we only have Sammy Moore and Harry Pell in that position."