Argentine Aguero, the Premier League's leading scorer with 14 goals, hobbled off after less than five minutes against Everton on Saturday.
"He will be out for four to six weeks," Pellegrini tod a news conference on Tuesday. "It will depend on his recovery. But our team doesn't depend on one player."
City can qualify for the last 16 if they win in Rome on Wednesday and CSKA Moscow do not beat Bayern Munich.
Pellegrini's side only have five points from their five Champions League games but can reach the knockout stage behind group winners Bayern Munich if everything goes their way.