The Frenchman suffered the blow just 16 minutes into the Gunners' 3-1 victory over Bournemouth at the Emirates last Sunday.
The 31-year-old, who joined the Gunners from Newcastle United in 2014, was making his first appearances in 12 months, but now faces an extended spell on the sidelines.
In Friday's press conference, Wenger told reporters: "It's a severe hamstring injury, yes. Six weeks, I think. It's frustrating for me but even more for him, he's a guy who fights hard, he has an exceptional attitude.
"He's absolutely disappointed, but he's a fighter, he will fight to come back."