The Croatia international suffered the injury during the Telekom Cup defeat against Bayern Munich on Sunday and the Bundesliga club have revealed that he will require surgery.
Wolfsburg are already without Patrick Ochs, Felipe Lopes and Christian Trasch due to injury and manager Klaus Allofs was left to rue another setback on Tuesday.
He told the club's official website: "These injuries are very unfortunate for us. But we have a wide squad, with which we have to compensate for these losses now.
"The important thing is that the healing process with each individual runs optimally and players can as quickly as possible to return to the team."
Perisic made 33 Bundesliga appearances for Wolfsburg last season and also scored twice in three games for Croatia in the World Cup last month.