The Gunners' £43million signing missed Sunday's 1-0 Barclays Premier League victory over Newcastle after being left at home nursing the injury, although he is expected to return to action early next month.
Manager Arsene Wenger said: "It is an inflamed shoulder. It should be maybe one more week, maybe less, I don't know, but not a long time."
Wenger was without both Ozil and Aaron Ramsey, who has a thigh problem, and Thomas Vermaelen and Nacho Monreal, who missed out through illness, at St James' Park.
However, his side returned to the top of the table courtesy of Olivier Giroud's 65th-minute header.