City are still waiting to learn the full extent of the injury but an absence of two weeks would put the Argentinian out of the derby against Manchester United on March 25.
Aguero underwent a scan on his return to Manchester and results are expected at the weekend.
The 25-year-old missed five games with a hamstring injury in February but Pellegrini is hopeful the problem is not as serious this time.
Pellegrini said: "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."
Aguero has already been ruled out of this weekend's Barclay Premier League trip to Hull and will face a battle to prove his fitness for the visit of Fulham the following Saturday.
The derby at Old Trafford comes three days after that.
Aguero's latest problem is a blow to City as they bid to recover from FA Cup and Champions League elimination to gain ground in the title race.
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 said: "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."
City are also still without striker Stevan Jovetic and defender Matija Nastasic but Pellegrini was hopeful that "maybe next week they can be fit".
Right-back Micah Richards is also out with an unspecified knock.
Pellegrini, speaking at a press conference to preview the Hull game, dismissed suggestions midfielder Jack Rodwell could be allowed to leave the club on loan.
Rodwell has failed to make an impression at City in two injury-hit seasons since arriving from Everton in a £12million deal.
The 23-year-old has been linked with an emergency loan switch to Wigan to cover for injuries.
Pellegrini said: "No, Jack will continue. Unfortunately for him he has had a lot of injuries during the year but he will continue now here."