Manchester City's top scorer pulled up hurt early in the second half of Saturday's 6-3 victory over Arsenal.
And speaking at a press conference ahead of Tuesday's Capital One Cup tie at Leicester, Pellegrini confirmed Aguero will miss a Christmas programme of fixtures including the visit of Liverpool on Boxing Day.
Pressed on exactly how long the Argentine would be missing, he said: "Maybe the doctor can tell you, but at this moment we don't know how long it will be."
Aguero and summer signing Alvaro Negredo have struck immediate success as a partnership this season, scoring 20 Premier League goals between them.
Pellegrini has Edin Dzeko as back-up while Stevan Jovetic, whose last appearance came in the Capital One Cup in October, is available after injury.
I imagine our opponents over the next few weeks will be mighty pleased to hear this.- bright and edgy