Aguero missed City's 3-0 win over Watford in the FA Cup third round on Saturday after suffering the problem late in the 3-0 win over Stoke on New Year's Day.
Manager Roberto Mancini initially said he hoped to have to his joint top-scorer back for next weekend's trip to Arsenal, but that now looks doubtful.
Sergio Aguero (on Twitter): "The studies confirmed I have a torn muscle.
"We have to keep on thinking positive and try to recover in the best way possible.
"For that, I've travelled to Italy where a specialist is treating me. I'll keep you up to date in how the injury evolves."
Aguero has 10 goals for City this season, level with Edin Dzeko.
Carlos Tevez replaced his fellow Argentinian in the line-up against Watford.
Source: Manchester City MAD