The Germany midfielder was substituted at half-time of Tuesday night's Champions League last-16 second-leg tie at the Allianz Arena and had already been ruled out of Sunday's derby with Tottenham.
"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 on Friday.
"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."
Ozil's absence is a blow following the news that Aaron Ramsey's return from a thigh injury has been delayed, with Jack Wilshere also sidelined with a broken foot suffered on England duty.
Sweden international Kim Kallstrom could be available for his debut at White Hart Lane 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."