The Argentina international, who recently missed eight matches with a calf problem, was forced off in the first half of City;s 5-1 victory at Tottenham Hotspur in the Premier League on Thursday.
“The doctor is seeing him – maybe one month, but we are not sure absolutely,” Pellegrini told reporters.
Aguero now stands to miss the first leg of City’s Champions League last 16 tie with Barcelona, as well as key league and FA Cup games against Chelsea.
However, with City having already amassed 115 goals in all competitions this season, Pellegrini believes his team can cope with Aguero’s absence.
“It’s very difficult. Sergio is a top player for us, but I think we can replace him,” said the Chilean.
“All the other strikers – Alvaro Negredo, Edin Dzeko and now Stevan Jovetic – can replace him.”