The Spaniard - who is amongst the favourites to win the upcoming Ballon d'Or title - is pivotal to City's style of play and serial success - and was left a heap against Arsenal prior to his 21st minute departure.
A defensive run alongside Arsenal midfielder Thomas Partey saw Rodri fall, clutching his right knee and needing to be hooked off with medical personnel providing immediate treatment as he left the pitch.
Tests undertaken on Monday uncovered the severity of the injury and a further round of examinations are expected to confirm that Rodri is set for months on the sidelines.
The 28-year-old has now been seen arriving in Barcelona for a consultation with injury specialist Dr Ramon Cugat who will determine the severity of Rodri's injury and timeline of absence.
Rodri has been spotted arriving at hospital in Barcelona for a consultation on a knee injury
One positive is that Rodri attended the meeting without the need for crutches or any walking aid and entered the premises supporting his own weight with a member of City's medical team also present.
However, it is widely expected that he will face a lengthy spell on the sidelines given the seriousness with which City are treating the injury as they seek to get a world-leading diagnosis.
Rodri's expected time out of action will require Pep Guardiola to find a new midfield system that accommodates for the loss of arguably his team's most important player.
He has not been involved in a losing team in the league since February 2023, with all three of City's defeats last season coming when the 28-year-old was absent and improving by going on to win the title when he was fit again.
The 2-2 Arsenal draw was Rodri's first start of the campaign after an extended summer break nursing an injury picked up in Spain's Euro 2024 final win over England.
Mateo Kovacic has previously deputised for Rodri in the past, while Ilkay Gundogan and Rico Lewis can also be used in more defensive midfield capacities.
City face a manageable run of immediate fixtures without the star midfielder as they play Watford, Newcastle, and Slovan Bratislava in their next three games.