During the final minutes of the game, Forest player Neco Williams aggressively shoved Marc Cucurella, causing him to collide with Chelsea coach Enzo Maresca.
The result was an altercation on the sideline between several players from both teams.
In a statement, the FA said: “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.
“Chelsea and Nottingham Forest have until Thursday, 10 October, to provide their responses.”