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.
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