The 31-year-old Croatian was absent from City's FA Cup final loss to Crystal Palace due to injury and also missed the final Premier League fixture of the season against Fulham through suspension, following a red card in the penultimate game against Bournemouth.
"Manchester City can confirm that Mateo Kovacic has undergone surgery on an Achilles injury," read an official statement. "The Croatian midfielder is now set to miss the FIFA Club World Cup as City head to the USA in June. Mateo will spend the summer rehabilitating from the operation and everyone at the club wishes him a speedy recovery."
The setback leaves Pep Guardiola short of midfield depth as City prepare to travel to Florida for the tournament, which kicks off on June 12. Compounding the issue, Kevin De Bruyne is expected to miss the tournament as he edges closer to a move to Napoli.
James McAtee will also be unavailable, having been granted permission to join England's Under-21 squad for the European Championship in Slovakia.
There is better news regarding Rodri, who returned to action at the tail end of the season after a brief injury layoff and is likely to be available for selection.
To bolster their midfield ranks, sources have told ESPN that City are working to complete the signing of Tijjani Reijnders from AC Milan. The deal is expected to be finalized ahead of the June 10 deadline for Club World Cup player registration.
City enter the tournament as European champions and are aiming to claim the Club World Cup title for a second consecutive year.