The Argentina international suffered the injury in Saturday's 6-3 Premier League win against Arsenal, and manager Manuel Pellegrini confirmed on Monday he will be without his leading goalscorer for a month.
"Sergio has a calf injury. The doctor can say how many weeks he will be out," said the Chilean.
"I don't know at the moment. I think he will be out for at least one month.
"(Micah) Richards, (Matija) Nastasic and Aguero are out (of Tuesday's Capital One Cup tie at Leicester). All the other players are okay, including (Stevan) Jovetic."
Aguero could miss as many as seven games, including the visit of Liverpool in the Premier League on December 26.
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