The Spaniard limped off during City's 2-2 draw against Arsenal in the Premier League on Sunday with a suspected anterior cruciate ligament tear in his right knee.
"Rodri will be out for a long time, a while. There are some opinions that it will be less than we expect, but unfortunately he was injured and right now we're waiting for the final phone calls from him and the doctors to know exactly what he has and the type of surgery he has to get," Guardiola said after City's 2-1 win over Watford in the League Cup on Tuesday.
Guardiola accepted the absence is a huge blow, but believes a City side that have won a record four consecutive Premier League titles can remain competitive.
"We will have a good season, I trust a lot in my players. I have the duty to find a solution," he added.
"Rodri is irreplaceable. When a team doesn't play with the best midfielder in the world for a long, long time of course it is a big blow but my duty is to find a solution so that we remain competitive as we have been for many years.
"When one player is irreplaceable you have to do it as a team and this is going to happen."
Rodri has been touted as a potential Ballon d'Or winner this year after his influential role in City's record fourth consecutive Premier League title and Spain's success at Euro 2024.
The former Atletico Madrid player has lost just one of his last 84 games for club and country.
