Pole Szczesny lasted just 18 minutes of Arsenal's 3-1 Champions League defeat by Barcelona on Tuesday and was replaced by Spaniard Almunia.
Arsenal, who face Premier League leaders Manchester United at Old Trafford in the quarter-finals of the FA Cup on Saturday, are already without Lukasz Fabianski for the rest of the season while Vito Mannone, who has been on loan at Hull City since October, is also injured.
"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," Wenger 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) but he is not available."
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