The France international suffered the injury during the 2-2 draw with Manchester City on September 13 after catching his studs in the turf.
Manager Arsene Wenger confirmed in the immediate aftermath of the game that the defender had sustained a sprain, but it was unclear how serious the injury was.
But on Monday, it was confirmed that the 29-year-old, who joined from Newcastle United during the transfer window, had been forced to undergo an operation and will be out until late December.
"He has had surgery and will be out for three months," Wenger told the club's official 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."
