Germany international Ozil, who cost 42.5 million pounds ($70.87 million) when he joined from Real Madrid in August, was substituted at halftime against Bayern Munich in the Champions League aggregate defeat on Tuesday.
"When the minimum is three, the maximum is six so let's say four weeks out," Wenger told reporters at a news conference of his playmaker's prognosis.
"Ozil had a very good game against Everton but he was handicapped early on in the Bayern game."
Arsenal have a number of injury concerns as they prepare for Sunday's north London derby at Tottenham Hotspur - a game they need to win to stay in touch in the Premier League title race.
Aaron Ramsey, who has been out since December with a thigh injury, had been in contention for a return against Spurs but that has now been delayed.
"He still has recurrent pains in his thigh, we have to be very cautious with him," Wenger said.
Better news for the Gunners is the return to fitness of defender Nacho Monreal and midfielder Kim Kallstrom, who has yet to make an appearance since joining in January. Defender Kieran Gibbs and striker Yaya Sanogo may also be fit to feature on Sunday.
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