The striker is currently in Italy undergoing treatment on the injury and is likely to miss his side's Premier League fixture against Arsenal next Sunday
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 approximately four to six weeks with the problem.
"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.