Fabregas was substituted in the 69th minute of the 2-0 loss in Portugal with his team mate Emmanuel Eboue also suffering a knee injury.
"Eboue will be out for a while and we will have to asses Fabregas tomorrow (Wednesday)," Wenger told the club's website after the match.
"It could be two to three weeks. It is very disappointing because I had a hesitation to play him (Fabregas) before the match started. I took the gamble and it backfired on us."
Arsenal face Aston Villa in a Premier League clash on Saturday and Wigan Athletic in the League Cup quarter-finals on Tuesday.
NEWS:Fabregas injured as Braga shock Arsenal
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