After reacting to a challenge from Morgan Gibbs-White in the corner of the field, the centre midfielder was sent off.
After the Forest player shoved him, the Man City player turned around and grabbed Gibbs-White by the neck.
Rodri received a straight red card after a VAR review for violent behaviour, leaving Pep Guardiola’s team with 10 players on the pitch.
As a result, the Spain midfielder will miss the forthcoming matches against Newcastle, Wolves, and the Arsenal due to a three-match suspension.
The match against Mikel Arteta’s team, which is set for October 8, may be crucial in the Premier League title fight this year.
The fact that City had to play practically the entire second half with 10 men as a result of Rodri’s dismissal put them under significant pressure.
The treble-winners took the lead in the first half thanks to goals from Phil Foden and Erling Haaland, but the numerical disadvantage allowed Forest to attempt to get back into the game.