The midfielder was taken off in the first half of City's Premier League game against Arsenal last weekend and the club have announced that the player will require surgery for the problem - although it is not yet clear how long he will be on the treatment table for.
A statement posted on the club website said: "Manchester City can confirm that Rodri has suffered a ligament injury to his right knee.
"The midfielder travelled to Spain to seek specialist consultation this week, following initial tests in Manchester.
"Assessment remains ongoing to ascertain the full extent of the injury and expected prognosis."
Rodri has been a pivotal player for Pep Guardiola's team in recent seasons and the coach expressed hope that the injury wouldn't rule the Spain international out for the rest of the campaign.
Speaking prior to City's statement, Guardiola said: "Still, we don't have the definitive. He'll be out for a long time, a while, but there is some opinions that maybe it will be less than we expect.
"Unfortunately he was injured. Right now, still, I cannot tell you [how long] because we're waiting the last phone calls from him and the doctors to know exactly what, definitely, he has and the type of surgery that he has to get."
Guardiola thinks that Rodri is "irreplaceable" but backed his team to carry on performing in his absence.
The manager said: "We don't want this but we will still have a good season. I trust a lot in my players, I have a duty to find a solution.
"Rodri is irreplaceable and the team won't play with the best midfielder in the world for a long, long time. Of course it's a big, big blow for us.
"But it's football, it's happened and my duty is to find a solution, to be competitive like we have been for many years."