Aguero limped off during the 5-0 victory over Burnley and after travelling to Barcelona on Tuesday to be examined by Dr. Ramon Cugat, the 32-year-old required an operation.
Manchester City Pep Guardiola told a Zoom news conference earlier on Wednesday that he wasn't sure when Aguero would return to the pitch.
"Once he finishes maybe we'll know exactly the time when he can come back and join us and play with us," Guardiola said.
Aguero is expected to miss City's last eight Premier League games, including the trip to Chelsea on Thursday, but there is still hope he could return in time to feature against Real Madrid in August in the delayed round-of-16 second leg tie.
UEFA have scheduled the remaining round-of-16 fixtures for Aug. 7 and 8.
City face Chelsea at Stamford Bridge on Thursday night but Guardiola said, with little left to play for in the league, he will prioritise Sunday's FA Cup quarterfinal with Newcastle United at St James' Park.
"We can't deny that we have one eye on Newcastle," he said. "Chelsea and Liverpool are prestigious but Newcastle is one game. A final. We have one eye.
"It depends on the physical condition, the minutes they have played. We take a look a little bit at what is going to happen, not just Chelsea."