The 2024 Ballon d'Or winner, who was named the player of the tournament as he captained Spain to World Cup glory this month, had been experiencing discomfort in his back before finally opting for surgery.
"The midfielder had been feeling discomfort for some time but has now undergone a procedure to address the issue and will now begin a short period of rehabilitation," City said in a statement.
City did not give a timeline for Rodri's return but British media reported he may miss the start of the league season, which kicks off on August 21st.
The 30-year-old Rodri, who has suffered serious knee injuries during his career, has one year left on his City contract and has been linked with a move to Real Madrid.