Ozil, who joined Arsenal from Real Madrid for a club-record fee on the final day of the close-season transfer window, suffered the injury in their 3-1 win over West Ham United on Thursday.
Ozil misses Sunday's match at Newcastle United and their match against Cardiff City on Jan. 1. He is also a doubt for their FA Cup third round clash against local rivals Tottenham Hotspur on Jan. 4.
"I would have loved him here (at Newcastle) but he had a shoulder problem, he fell on his shoulder. He will be out for two-to-three games," Wenger told Sky Sports.