Manchester City confirmed on Tuesday that Rodri underwent a successful minor operation on his back.
The midfielder had been struggling with some discomfort for a while, City said in a statement on their official website. Surgery has now addressed the problem, and he will begin a short period of rehabilitation.
City promised further updates on Rodri's recovery via the official website, but stopped short of putting a timeframe on how long the Spain star will be sidelined.
Real Madrid and Barcelona have both been linked with the 28-year-old during the ongoing summer transfer window.
His contract at the Etihad expires next summer. That means Rodri would be free to agree a move with any club from next January.