The striker had been complaining about the problem all week but it was hoped that the injury would fade away.
Peeters told De Gelderlander: "I felt it straight away, it just shot up my whole leg, this will cost me at least a few weeks out of the team."
Vitesse signed the big Belgian from Erdevisie rivals Roda JC Kerkrade for £4.3 million in 2000 and the injury could not have come at a worse time for the coach Mike Snoei.
The Gelredome side already have fellow striker Mamadou Zongo out, while Kalle Sane and Eldridge Rojer are not yet ready to resume training, leaving Snoei short of attacking options.
Jhon Van Beukering has been loaned to FC Zwolle meaning that Hannover 96 target, Matthew Amoah and Emile Mbamba are practically guaranteed starting places.
Vitesse's lack of front players means that Amoah is almost certain to remain with the Dutch side.
