The 23-year-old French full-back sustained the injury during the Champions League quarter-final first leg at Villarreal on April 7 and has missed Arsenal's last 10 matches.
"It is finished for Gael. We would have put a little more pressure on the recovery period had we gone to the Champions League final, but now we will not take a gamble," Wenger told the club's website.
Arsenal, knocked out of the Champions League by Manchester United on Tuesday, are fourth in the Premier League with three matches remaining.
They face Chelsea, who were also knocked out of the Champions League this week, in the Premier League at the Emirates Stadium on Sunday and would move to within three points of their west London rivals with victory.
Andrei Arshavin, who was cup-tied for the Manchester United match, should return to the side to face Chelsea, managed by his Russian international coach Guus Hiddink.
Wenger said Arshavin had a touch of flu on Thursday and missed training but should be fit to play.
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