The Argentina international picked up the injury during the second half of City's 3-0 victory over Stoke in the Premier League on Tuesday and is now set to be sidelined for up to four weeks with the problem.
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"The studies confirmed I have a torn muscle. We have to keep on thinking positive and try to recover in the best way possible" Aguero posted on Twitter.
"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 is likely to miss around five Premier League matches for City, including fixtures against Arsenal next Sunday, and a home tie against Liverpool on February 3.
Roberto Mancini's side are seven points behind Manchester United in the Premier League, while a bust-up between the Italian and Mario Balotelli on Thursday has put the forward's future at Eastlands in doubt.
Aguero has scored 10 goals in 24 appearances in all competitions for City this season.