The left-back limped out of Wednesday 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.
"He was an important player for us going forward and the game we wanted to play. It's a shame he's out for the next three weeks."
Gibbs will miss Saturday's meeting with Stoke and a further Premier League clash against Sunderland, while he could also be a doubt for the Champions League encounter with Bayern Munich.
Wenger admitted he may make a move for a replacement on the final day of the transfer window on Thursday.
One man Wenger admits will not be coming to the Emirates is David Villa.
The Barcelona man has been a target of Wenger's but a deal has failed to materialise and when asked if it was dead, he said: "Yes."