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.
The UK's only bonobo baby born at Twycross Zoo
University Hospitals of Leicester NHS Trust part of national investigation
Yellow warning for wind in Loughborough and Charnwood
Leicestershire team raise funds for a tranquil garden space for victims and survivors of sexual assault
New bigger Primark store opens in Loughborough
Fosse 107 helps celebrate Charnwood's community heroes
Three arrested for drugs offences following collision on Epinal Way
