The 28-year-old was substituted midway through the first half at the Etihad Stadium after what appeared to be minor contact from Thomas Partey, and was replaced by Mateo Kovacic.
All three of City’s defeats during their historic fourth consecutive Premier League title-winning season last campaign came without the Spain international in the team, underlining the importance of his role in Pep Guardiola’s side.
He is due to undergo further tests but it is reported that early indications show his season could be over after only five league games.
City have been contacted by the PA news agency.
Guardiola, whose team moved back to the top of the table after John Stones’ stoppage-time equaliser against the Gunners, has Kovacic and Ilkay Gundogan as possible stand-ins, while England international Rico Lewis can also play in the role.
Speaking after Sunday’s match about the likely severity of Rodri’s injury, Guardiola said: “I don’t know yet. I didn’t speak with the doctors.
“Rodri is a strong man. If he leaves the pitch, then he felt something, otherwise he stays there.”
Rodri joined City in 2019 from Atletico Madrid and has made 260 appearances in all competitions, helping the club to four titles as well as the Champions League in 2023.
He was part of the Spain side that won Euro 2024 in Germany defeating England 2-1 in the final.
