The club has not made any official statements regarding the specifics of the injury, although British media reports suggest that the Spanish international may have suffered an ACL injury, which could result in a lengthy absence from the squad.
Various segments of the Spanish media shared footage on social media showing Rodri's arrival in Barcelona on Monday.
Should Rodri be sidelined for an extended period, it would significantly hinder City's prospects of securing the Premier League title for a record fifth consecutive season. Currently, City holds a one-point lead in the league after five matches.
Rodri, a leading contender for the 2024 Ballon d'Or, is considered one of City's most crucial players due to his role in shielding the defense and orchestrating the team's passing strategy.
He exited the field in the 20th minute of the 2-2 draw against Arsenal at the Etihad Stadium on Sunday after injuring his right knee while contesting with Arsenal's Thomas Partey during a corner kick.
Just a week prior, Rodri expressed concerns that top players might soon consider striking due to the increasing number of matches being scheduled as new competitions are introduced to an already congested football calendar.