Walker suffered the injury in the first half of City's 6-3 victory against Manchester United at the Etihad Stadium on Sunday.
No timescale has been put on his return but it is understood City believe he still has a chance of playing at the World Cup, which gets under way for England against Iran in Qatar on November 21st.
"Kyle Walker has undergone surgery after suffering a groin injury to his left leg during the first half of our 6-3 win over Manchester United on Sunday," a City statement said on Thursday.
"The surgery was successful and a more detailed prognosis will be provided in due course."
Walker tweeted a picture of himself in his hospital bed alongside a message saying: "As players we have to appreciate injuries are part and parcel of the game we love.
"My operation on Tuesday was a success and now I can concentrate on my rehab and getting back to full fitness."
Walker has 70 caps for England and was expected to be a key figure in Gareth Southgate's squad at the World Cup.
He offers tactical versatility to Southgate, who has used him at right-back and as a centre-back in a three-man defence.
City manager Pep Guardiola said after his side's 5-0 win against Copenhagen in the Champions League on Wednesday that Walker would be out for a "while".
"I know how important the World Cup is for the players but honestly I don't know right now," he added.
If Walker is ruled out of the World Cup, it could open up a place in Southgate's squad for Liverpool right-back Trent Alexander-Arnold.
Alexander-Arnold was unused by Southgate in England's recent Nations League matches against Italy and Germany, sparking a debate about the manager's treatment of the Liverpool star and his perceived defensive weakness.
Southgate opted to leave Alexander-Arnold on the substitutes' bench against Italy and omitted him from the matchday squad for the Germany game.
England must submit their 26-man World Cup squad by November 13th, giving Walker just over a month to prove his fitness.
