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.
Deadline approaching for Leicestershire secondary school applications
Eleven arrested in Leicestershire vehicle crime crackdown
Leicestershire recycling centres launch ReHome Zones for unwanted household items
Hinckley Leisure Centre Car Park to be closed for one day
Police investigate seven courier fraud reports across Leicestershire
Four men bailed after Heather firearms incident
Police seek to identify three women after shop theft in Ibstock
Should the school summer holidays in Leicestershire change?
