The summer signing hobbled out of the 5-1 win over Atalanta in the UEFA Champions League on Tuesday in the first half, adding to a growing list of injuries for the Premier League title holders.
After the game, Guardiola provided more details on the issue accrued by the Spain international and said the worst-case scenario is that Rodrigo spends four weeks on the sidelines, per Dom Farrell of Goal.
"Tomorrow [Wednesday] we will know," said the City manager. "Hopefully [Rodrigo will be out] between 10 days if it is not broken [torn]. If it is broken, it will be three weeks or one month. It is hamstring, it looks like. When a guy runs and puts his hand in the hamstring position, it is a hamstring."
Rodrigo has played as a centre-back for the last couple of matches, with City light on options at the heart of defence. On Tuesday and in the Premier League clash with Crystal Palace on Saturday, he partnered fellow midfielder Fernandinho in a makeshift defensive pair.
Per football writer Zach Lowy, although City have a squad packed with talent, they've had some key players absent due to fitness issues:
John Stones, who has recently recovered from a thigh problem, was brought on for Rodrigo in the win over Atalanta and told BT Sport (h/t Farrell) after the game he was impressed with how the former Atletico Madrid man fared in an unfamiliar role:
"It's the first season for Rodri, he's slotted in brilliantly in a new league, a different [one] for him, and he's breezed it.
"Credit to Fernandinho, he's helped him along. We work on playing different positions in training all the time, knowing everyone's jobs and the roles on the pitch, so you can almost play blind when you have the ball."
Sam Lee of The Athletic praised the manner in which the two holding midfielders acquitted themselves in deeper roles:
Since joining City in the summer, Rodrigo has been a big hit for the team, offering a steady presence with his passing and defensive positioning at the base of midfield.
Per WhoScored.com, he's also adept at slaloming away from opposition players:
Players with a 100% dribble success rate in Europe's top 5 leagues this season (10+ dribbles) Rodri - Man City (12/12) Arthur - Barcelona (14/14) T. Partey - Atletico (11/11) M. Grujic - Hertha (12/12) A. Lusamba - Nice (11/11) H. Maïga - Metz (13/13) B. Soumaré - Lille (11/11) https://t.co/dUEtm7lBQe
Stones getting back to full fitness is a boost for City. Although he had his struggles early in the campaign, City supporters will be glad to see another recognised centre-back available ahead of a busy period.
The club will naturally hope for the best on Rodri, who has already established himself as a key member of Guardiola's side. Regardless of the severity of the injury, the 23-year-old may not be risked on Saturday when the champions welcome Aston Villa to the Etihad Stadium in the lunchtime kick-off.