The right-back sustained the injury during his side's 2-2 draw with Manchester City at the Emirates Stadium earlier this month.
Having now gone under the surgeon's knife, Wenger has revealed that his summer signing from Newcastle United is likely to be sidelined until January.
"He has had surgery and will be out for three months. A reasonable delay is three months," he told the club's official website. "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."
The Gunners are thought to have paid Newcastle £12m to secure the 29-year-old's services.