The midfielder hasn't recovered from the knee injury suffered in the Carling Cup final.
Arsenal confirm van Persie is out of Champions League clash with Barcelona
Van Persie was injured when scoring the equaliser in the Carling Cup final on Sunday, which Arsenal lost 2-1 to Birmingham City. The London club said he would be out for at least three weeks.
Arsenal take a 2-1 advantage to Spain for the return Champions League leg on March 8.