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.
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