The charges stem from a 1-1 draw between the two teams in the Premier League over the weekend.
"It's alleged that both clubs failed to ensure their players didn’t behave in an improper and/or provocative way around the 88th minute," the FA said in a statement.
Forest's Neco Williams had pushed defender Marc Cucurella at one stage of the game.
That resulted in others getting involved, including Levi Colwill of Chelsea and several Forest players.