The France international joined Arsenal from Newcastle United for 12 million pounds ($19.6 million) in July and has played only seven times for his new club.
He suffered the injury after falling awkwardly when Arsenal drew 2-2 with Manchester City on Sept. 13.
"He has had surgery and will be out for three months," Wenger told the club's website.
"A reasonable delay is three months. It all went well, but it can be a week or two earlier, or a week or two later, but it will be around three months.
"It is a blow, of course, how big it will be we will only know afterwards because it will be down to how well we replace him. We bought (Calum) Chambers for that."
Wenger has been criticised by Arsenal supporters for not having ensured sufficient cover at the back after allowing Thomas Vermaelen to leave for Barcelona.
The Gunners' defensive frailties were exposed when they lost 2-0 at Borussia Dortmund in the Champions League last week. But they kept a clean sheet in a 3-0 defeat of Aston Villa on Saturday, moving up to fourth in the Premier League.
Their next match is at home to Southampton in the League (Capital One) Cup on Tuesday before the north London derby with Tottenham Hotspur at the Emirates on Saturday.
(Reporting by Mike Collett; Editing by Robert Woodward)
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