Fabregas limped out of Wednesday's Premier League win over Stoke with a hamstring strain and will now miss Sunday's final at Wembley, where Arsenal are bidding to win their first silverware since 2005.
Wenger said he hoped Arsenal would go on to lift the trophy as a tribute to Fabregas, who is now battling to be fit for the club's Champions League second leg match with Barcelona on March 8.
"It is a very small injury but certainly Cesc will be out for Sunday," Wenger told Arsenal TV. "For how long beyond that I don't know, but definitely for Sunday.
"He is disappointed. We all feel sorry and sad for him. The only way we help him now is to win the Carling Cup as he contributed a lot in this competition."
Arsenal will also be missing England international Theo Walcott, who sprained an ankle against Stoke.
Wenger said Walcott was likely to face up to two weeks on the sidelines.
"He has a classic ankle sprain. We don't think there is any more damage to it, but it is still a sprain," he said.
"We are sad for him too. He is out for Sunday and maybe one or two weeks more."
We'll do it for injured Cesc, vows Wenger
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