The 24-year-old collided with Reading's Stephen Hunt in the first minute of the game at the Madejski Stadium.
Cech was transferred to the Radcliffe Infirmary's specialist neuro-surgical unit in Oxford on Saturday night.
"The operation was successful but it is too early for an accurate assessment of his condition," said a Blues statement.
Cech and his replacement Carlo Cudicini were both carried off during the game and were both immediately taken to hospital.
Cudicini was discharged on Saturday night after being knocked unconscious in injury time.
Blues boss Jose Mourinho said immediately after the game that he was deeply unhappy with Hunt's challenge and said Cech was "lucky to still be alive".
The Chelsea statement continued: "Chelsea have reviewed the video of both incidents.
"We endorse the post-match comments of Jose Mourinho regarding the seriousness of these incidents.
"Chelsea will be writing to the Football Association with our observations."
Reading boss Steve Coppell said he was confident neither Hunt nor Sonko were deliberately trying to hurt the Chelsea keepers.
"I welcome Jose saying the FA should review them," he said. "We apologise to Chelsea for the injuries but I still think both players will be vindicated."
Arsenal goalkeeping legend Bob Wilson said he was disappointed by Mourinho's comments and agreed with Coppell that there was no intent shown by Hunt and Sonko.
"I was sad to hear Jose's comments after the game," Wilson told Five Live's Sportweek programme.
"Keepers expect to get bumps and bruises, it's part of what we do. We don't want to be protected all the time."
Chelsea face Barcelona in the Champions League on Wednesday, with third-choice keeper Hilario set for a start.
Hilario, 31 next Saturday, joined Chelsea on a free transfer last June from Portuguese side Nacional but he has yet make his debut for the Premiership champions.