Pole was forced off in Champions League defeat to Barcelona
The Pole picked up the injury in the 3-1 defeat to Barcelona on Tuesday night and had to be replaced by Manuel Almunia after just 19 minutes.
And with Lukasz Fabianski and Vito Mannone - on loan at Hull City - on the sidelines, Wenger has reiterated that he will look to sign a goalkeeper on an emergency loan deal.
"We need now an experienced goalkeeper as cover for Almunia because Mannone is out for six weeks so we cannot call on him," he told Arsenal TV Online.
"Mannone is here at the training ground having treatment but he cannot play for the next six weeks. We can call him back [from Hull City] but he is not available.
"We have Wojciech out, in my opinion for six weeks. We have Fabianski out for the rest of the season. We need absolutely some cover in goal."
With three of Arsenal’s goalkeepers now injured, Wenger has called on Almunia to stake his claim for a regular spot in the starting line-up.
"He is very professional, [has a] very dignified attitude and overall he has done very well," he said.
"Yes, he has done quite well when he came on [against Barcelona] and was quite busy in the final part of the game and he did very well.
"When I took Jens Lehmann out, who [had] made only one mistake, and put Almunia in, Lehmann came in the next day and fought even harder. That's what I believe our job is about."