Leven took the knock on Thursday and scans have since revealed he has fractured a metatarsal.
The former Rangers trainee has scored eight goals for the Dons this season and will now miss the League One play-offs semi-finals.
The club's head of sports medicine Simon Crampton told the club's official website: "Peter was injured in an innocuous incident in training.
"Unfortunately initial x-rays demonstrated a fracture in his foot."
The injury could mean Leven has played his last game for the Dons as his contract expires this summer with no new deal yet agreed.
Source: PA
Source: PA