Players and staff of both teams squared up to each other during second half stoppage time following a challenge by Leicester’s Ricardo Pereira on Chelsea’s Ben Chilwell.
Pereira and Leicester’s unused substitute Daniel Amartey, who courted controversy by throwing Chelsea’s pennant to the ground during the Foxes FA Cup final celebrations, were booked after the scuffle.
The FA charged both teams for failing to control their players and have now issued them with £22,500 fines each as punishment.
A statement from the FA on Tuesday said:"Chelsea FC and Leicester City have been fined £22,500 each after admitting a breach of FA Rules E20.1 following their Premier League fixture on Tuesday 18 May 2021.
"Both clubs admitted that they failed to ensure their players and club officials conducted themselves in an orderly fashion and refrained from provocative behaviour during the 93rd minute of the fixture."
Chelsea defeated Leicester 2-1 on the night, helping them to eventually pip the Foxes to the final Champions League spot on the final day of the season.