The Germany international - a £42million buy from Real Madrid last summer - suffered the problem during Tuesday's 1-1 last-16 draw at Bayern Munich which saw Arsenal exit the Champions League.
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."
Arsenal striker Nicklas Bendtner was not included in the travelling squad for the Bayern Munich tie because of a minor knee injury.
The Denmark international was allegedly involved in an drunken incident in Copenhagen, for which Wenger confirmed he would face sanctions from the club following the unauthorised trip home.
The 26-year-old is reported to have threatened a taxi driver, then unbuttoned his trousers and rubbed against the car, during an incident in the Danish capital while his team-mates were playing against Munich.
Wenger said: "Honestly I don't know really what happened because I haven't spoken to him. The only thing that is for sure is he had nothing to do in Copenhagen. Nobody gave him any permission to go to Copenhagen and he will be fined for that.
"For the rest, he has created some trouble there I don't know, I will speak to him today."
Bendtner has not played for the Gunners since February 2, but did start for Denmark in the Wembley friendly against England last week.
Asked whether this was the 'final straw' for the player, Wenger said: "He is at the end of his contract at the end of the season."
Arsenal head to Tottenham looking to pull themselves back into the Premier League title race.
Following their FA Cup quarter-final win, the Gunners hold a match in hand on leaders Chelsea, but are seven points off top spot now down in third place.
Wenger is expecting a focused display from his side in what will be a heated atmosphere.
"It has been always difficult at White Hart Lane, but we are in a position where of course we want to win the game, because after (losing at) Stoke, it is very important," Wenger said.
"We had a good result against Everton, we had a good result even at Bayern, but that we continue and have no weak moment any more until the end of the season."
Wenger added: "It is a difficult ground to go to for everybody. We had good and bad memories there, so let's make sure the good comes out on Sunday."