Manchester City have confirmed they will not appeal the red card given to Rodri in their 2-0 win over Nottingham Forest on Saturday.
The three-match ban for violent conduct means that the Spaniard will miss City's important trip to the Emirates Stadium to face Arsenal at the start of October.
Before then, Rodri will also miss the side's EFL Cup tie at Newcastle United on Wednesday, and their trip to Molineux to face Wolverhampton Wanderers at the weekend.
The midfielder was dismissed by referee Anthony Taylor inside the first minute of the second half after a scuffle with Forest's Morgan Gibbs-White.
After some pushing and shoving, Rodri put his hands around the neck of the Forest man, who then went to ground.
Taylor wasted no time in brandishing the red card, but despite playing with a man light, City still held firm for the three points.
Man City manager Pep Guardiola admitted that Rodri has "learnt his lesson" and called on his players to keep their composure and control their emotions better in similar scenarios.
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Post-match, when speaking on the incident, Guardiola said: "Rodri has to control himself and his emotions. This is what he has to do. I can get a yellow card but Rodri cannot get a yellow card. I do not play. The guys inside have to be careful."
In Rodri's place may come Kalvin Phillips, who was brought on shortly after the red card at the Etihad at the weekend.
The former Leeds United man got his first 90 minutes under the belt this season in England's 3-1 win over Scotland earlier this month.
Another start against Newcastle in the cup this week could bring Phillips more up to pace, after playing just 15 minutes in a City shirt this season before Saturday.
Rodri can still play in Man City's Champions League clash with RB Leipzig, which comes just days before the Arsenal encounter, but Guardiola will need an alternative for the trip to North London.
Bernardo Silva is also expected to be missing from the City midfield for the next few weeks, but Mateo Kovacic is back in training.
The Croatian midfielder will face a late fitness test before their trip to St James' Park on Wednesday, and will battle with Phillips and Matheus Nunes for a starting spot.
