The teenager was forced off against West Ham at half-time of Sunday’s 3-1 loss, in which Chukwuemeka scored his first goal for the club.
Standard Sport understands Chukwuemeka is expected to be out for six weeks after hurting himself in a collision with Emerson Palmieri at the London Stadium.
Chukwuemeka could miss up to seven games on the sidelines, with the trip to Arsenal on October 21 after the second international break the most likely return date.
A statement read: “Carney Chukwuemeka sustained an injury to his left knee during our game against West Ham United on Sunday.
“Last night Carney underwent surgery and will now begin his recovery.
“The 19-year-old will work with the club’s medical department on his rehabilitation at Cobham.”
Chelsea have eight senior players on the sidelines, a record only better than Aston Villa and Sheffield United.
Reece James and Trevoh Chalobah suffered hamstring injuries in training last week, joining Christopher Nkunku and Wesley Fofana after the pair suffered major pre-season knee injuries.
Armando Broja, Benoit Badiashile and Marcus Bettinelli all remain out from last season.
Chelsea’s injury record is a wider concern after a radical overhaul of the medical department saw long-serving heads of department Thierry Laurent and Paco Biosca leave early last season.
The Blues then suffered the worst injury record of any Premier League team suffering 48 injuries, missing a combined 1,836 days and 216 games during the 2022/23 season.