The Spaniard is no stranger to a yellow card but received his marching orders for the first time in his City career in the 2-0 win.
The holding midfielder had been having a superb start to the season, having registered two goals and one assist in six league games.
He also had a hand in Phil Foden's opener against Forest before an altercation with Morgan Gibbs-White saw him see red.
Rodri had reacted angrily to a shove from the England U21 European champion, turning around and grabbing Gibbs-White by the neck.
After a VAR review for violent conduct, Rodri was given a straight red card and now will be sidelined for a pivotal point in City's season.
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How long is Rodri suspended for?
Rodri will serve a three-match suspension as his red card was due to violent conduct.
As a result, he will miss City's next three domestic fixtures which starts on Wednesday in their Carabao Cup third-round match at Newcastle.
Rodri will then be missing for the trip to Wolves in the Premier League three days later.
The reigning Champions League Player of the Season can return for the visit to RB Leipzig on October 4 as domestic bans do not carry over to Europe.
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But crucially that means the third and final game of Rodri's suspension will come in their clash with rivals Arsenal on October 8.
And Rodri, who has built a reputation as a big-game player, will be a huge loss to City in their biggest game of the campaign so far.
Speaking after the red card, 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."
Two seasons ago, Rodri was City's match-winner at the Emirates against Arsenal but his ban ensures there will be no repeat in October.