The 26-year-old Germany international picked up the problem during the 2-0 defeat by Chelsea earlier this month and is set to be out until the end of November.
Wenger also confirmed that defender Laurent Koscielny is out of Saturday’s clash with Hull City with an Achilles injury.
However, Theo Walcott, Serge Gnabry and Mikel Arteta will all be back in the squad for this weekend’s game.
Wenger said: “Ozil is out for at least six weeks. The positive news is Theo, Serge and Mikel are back in the squad.
“Koscielny will not be available with an Achilles problem. He is not in contention for Saturday, but he will not need to have surgery.”
Asked about the fitness of midfielders Aaron Ramsey (hamstring) and Tomas Rosicky (calf), Wenger added: “Ramsey will be back in full training on Monday and will be in the squad for Anderlecht.
“Rosicky came back with a kick on the calf but he should be available for Saturday.”
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