The Ballon d’Or winner limped out of City’s victory over Brentford in their last match before the recent international break after just 21 minutes with a thigh injury.
It is the latest setback to have been suffered by the Spaniard, who missed most of last season following knee surgery.
Rodri was injured in the meeting with Brentford (Steven Paston/PA)
He has completed the full 90 minutes for City on just two occasions this term.
Manchester Pep Guardiola said at a press conference: “He is not ready for tomorrow.”
Asked how long the 29-year-old could be out for, Guardiola said: “I don’t know.”