The left-back limped out of last night's 2-2 draw with Liverpool suffering from the problem and was replaced by Andre Santos.
"He has a thigh strain that rules him out for the next three weeks. It's a blow for us of course," Wenger said.
His Liverpool counterpart Brendan Rodgers was pleased with the response of his players after their FA Cup exit at the hands of Oldham at the weekend.
"It was a wonderful game," Rodgers said. "Normally you would be bitterly disappointed not to have won, but I can only be proud of the players, I thought they were absolutely magnificent.
"I thought Jordan Henderson was brilliant, he scored a magnificent goal tonight that was about his sheer desire.
"He will be a terrific player for Liverpool, he is learning the game tactically all the time and the last few months he has been brilliant."
Wenger admitted his side's defensive problems were again exposed.
"We have shown great quality and spirit, but we were nervous defensively. Going forward I felt we were absolutely outstanding all night," he added.