New manager Enzo Maresca revealed on Friday that the procedure would take place on Monday, addressing a lumbar issue the 30-year-old had been carrying for some time.
"He needs a holiday, he needs to rest and recover and then he will be back with us," Maresca said, with the club confirming no timeline has been set for his return.
Manchester City open their season with the Community Shield against Arsenal on 16 August before hosting Bournemouth in their Premier League opener a week later.
Rodri's back problem had reportedly been managed through the World Cup so he could remain available for Spain, where he lifted the trophy as captain and was named player of the tournament after winning the Golden Ball, adding to the Ballon d'Or he claimed in 2024. Injury problems have dogged his last two campaigns at City, with a serious anterior cruciate ligament tear having ruled him out for the bulk of the 2024-25 season before he returned to help the club through last term.
The 30-year-old, who has a year left on his contract, has also been strongly linked with a move to Real Madrid following his World Cup exploits, though City's stance on any departure has not been detailed.
Maresca, who takes charge for the first time following Pep Guardiola's decade in the Etihad dugout, dismissed the transfer talk when asked about it, insisting speculation was to be expected around a player of Rodri's stature after such a tournament. The Italian previously worked as part of Guardiola's coaching staff before taking charge at Leicester and Chelsea.
Elsewhere at the club, defender Josko Gvardiol has signed a new five-year contract that will keep him at Manchester City until the summer of 2031, extending a stay that has already brought six major trophies since his £77m move from RB Leipzig in 2023.