Wenger confirmed Ozil would definitely be out of Sunday's north London derby with Tottenham, but was not able to put a specific time frame on recovery.
"We lose Ozil, who has been injured for Sunday, I don't know how long he will be out but it looks a minimum of three weeks," Wenger said at Friday morning's press conference.
"When the minimum is three, (then) the maximum is six. I am not specialist enough to know, it is a grade two hamstring (tear), so let's say four weeks."
Midfielder Aaron Ramsey's return from a thigh injury has been delayed, and England international Jack Wilshere is sidelined with a broken foot.
Sweden international Kim Kallstrom could be in contention for his debut after signing on loan from Spartak Moscow with a back injury while full-back Nacho Monreal is also available again.
Wenger added: "It is of course a blow, but I am confident we have the quality to deal without him (Ozil). We have many creative players who can take over to produce quality performances."
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