Players from both sides were involved in a argument at the end of the Blues' 2-1 win.
The FA said both clubs admitted they failed to keep their players and staff under control and act in an orderly manner.
They were fined £22,500 each.
Regulation and Discipline update on @ChelseaFC and @LCFC pic.twitter.com/tUTNDCTW6Q
— FA Spokesperson (@FAspokesperson) June 1, 2021
Tensions had been high all game, fuelled in part by the FA cup final between the two teams which had taken place just two days earlier.
Leicester City won that game 1-0, although Chelsea fans were controversially denied a late equaliser by the Video Assistant Referee.
Tributes to former leader Nick Rushton
103 years since the official opening of the Carillon Tower and War Memorial.
British Heart Foundation announces closure of 150 Stores over two financial year
Carelessly Discarded Cigarette Sparks Serious House Fire in Measham
Work starts on new primary school
Tribute to man who died in Loughborough
How local government re-organisation looks in Leicestershire
New ticket barriers planned at Nuneaton station
