The Argentina international, who missed five games with a similar problem in February, was withdrawn at half-time of the Champions League defeat to Barcelona on Wednesday after feeling a twinge.
He underwent a scan upon his return to Manchester, with the results expected at the weekend, but an absence of two weeks would rule him out of the derby with rivals United on 25 March.
But Pellegrini, whose side travels to Hull on Saturday, hopes the problem is not as serious as before, saying: "Sergio will know on Saturday what he has. It is 48 hours after the exam when they will know exactly what he has.
"I really don't know, but I don't think it is really very serious. I am hopeful he will (only) be injured for a couple of weeks."
City have fallen nine points behind leaders Chelsea, but have three games in hand, while focusing on other competitions in the past three weeks.
Pellegrini added: "We need to work hard with everyone, with the staff, with all the players. Now we must try to fight for the title in the Premier League."