The Czech international injured himself in training on Thursday. He is likely to miss the home games with Liverpool, Newcastle and possibly the Champions League tie with Hamburg.
Rosicky joins Freddie Ljungberg (calf), Julio Baptista (hamstring), Lauren (knee) and Abou Diaby (ankle) on the injured list.
Manuel Almunia is available for Sunday's game with Liverpool despite suffering concussion at Everton in midweek.
Copyright 2016 The Arsenal Football Club plc. Permission to use quotations from this article is granted subject to appropriate credit being given to www.arsenal.com as the source