Walker suffered what manager Pep Guardiola had initially said was an abdominal problem during Manchester City’s 6-3 victory over Manchester United on Sunday and was forced off before half-time.
However, in a statement on Thursday the club confirmed Walker had gone under the knife to resolve an issue with his left groin.
Speaking after City’s 5-0 victory over Copenhagen in the Champions League last night, boss Guardiola said he was unsure whether the full-back would recover in time for the tournament, which is now little more than six weeks away.
“He’ll be a while out,” Guardiola said. “I don’t know [how long]. I can’t say anything else. We have to speak to the doctors. Hopefully, he can get back like Kalvin [Phillips].
“I know how important the World Cup is for the players.”
Southgate is blessed with a number of options at right-back, including Trent Alexander-Arnold, Kieran Trippier and Reece James, who appears to be leading the race for the position after starting both Nations League games during last month’s international break.
However, Walker has excelled on the right side of a back-three at each of the past two major tournaments and has been a key part of England’s defensive solidity under Southgate.
The 32-year-old remains a likely starter if fit for the group stage opener against Iran on November 21 and his absence would rob England of a degree of tactical flexibility.
Southgate already has concerns over John Stones, who is out with a hamstring injury, though the centre-back is expected to return to action this month.
The England coach has major decisions to make at the back, with Harry Maguire out of form and out of the Manchester United side, while Luke Shaw and Ben Chilwell are in need of more regular playing time at their clubs.