Leicester's Matty James and Villa's Ciaran Clark were sent off in the match.
Both clubs admitted an FA charge of "failing to ensure their players conducted themselves in an orderly fashion and/or refrained from provocative behaviour".
Villa's case will be heard by an Independent Regulatory Commission.
Players clashed on the pitch during Leicester's 1-0 win following a tackle by James on Jores Okore. There was then a confrontation between the benches as the players walked off at full time.
It is the third time Villa have been found guilty of the offence this season.
They were fined £20,000 and £30,000 for failing to control their players in games against Tottenham and Manchester United respectively.