Pep Guardiola fears Manchester City could be without Rodri for up to a month after he sustained a hamstring injury during the 5-1 Champions League win over Atalanta.
Spain international Rodri, who became the Premier League champions' record signing when he joined from Atletico Madrid in July, was deployed at centre-back alongside Fernandinho for the second time in the space of a week on Tuesday.
Having helped Guardiola's side keep a clean sheet in the 2-0 win over Crystal Palace on Saturday, the City boss again went with the midfield duo in central defence, with John Stones left on the bench.
But, in getting back to challenge Atalanta captain Alejandro Gomez, Rodri instantly signalled to the bench that he needed attention.
Guardiola confirmed after the match that his player's complaint was hamstring-related, with the severity to be determined.
"Tomorrow [Wednesday] we will know," City manager Guardiola said. "Hopefully [Rodri will be out] between 10 days if it is not broken [torn].
"If it is broken, it will be three weeks or one month.
"It is hamstring, it looks like. When a guy runs and puts his hand in the hamstring position, it is a hamstring."
Stones, only recently back from his own spell on the sidelines with a thigh injury, came on to provide a more conventional option at the heart of a defence still awaiting the return of Aymeric Laporte from knee surgery.
"It's the first season for Rodri, he's slotted in brilliantly in a new league, a different for him and he's breezed it," the England international told BT Sport .
"Credit to Fernandinho, he's helped him along. We work on playing different positions in training all the time, knowing everyone's jobs and the roles on the pitch, so you can almost play blind when you have the ball.
"It's been good to be back out on the pitch for me on a personal note, [but I'm] upset to see Rodri has a little injury. We'll see how it is."
Before kick-off, City announced they were waiting to discover how serious a knee injury suffered by left-back Oleksandr Zinchenko might prove to be.
Winger Leroy Sane, meanwhile, is continuing his rehabilitation from cruciate ligament damage sustained during August's Community Shield clash with Liverpool.