Leicester's Matty James and Villa's Ciaran Clark were sent off in the game.
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.

About Â£11m will be spent on the upgrade at the Hearts ground. The current main stand was built in 1919.
The club hopes work will begin next month.
Hearts owner Ann Budge said last month that she hoped the work would be completed in September 2017. The new stand will increase the capacity to more than 7,200 from 4,720.
Ms Budge said the current stand was still useable but not up to the standards that fans expect.
The plans involve demolishing large sections of the existing main stand, and the ticket offices and shops.

A BBC crew recorded a party member remarking at a meeting that Golden Dawn members had not beaten radical left MP Dimitris Stratoulis hard enough.
The party sued Mr Stratoulis when he accused them over the attack.
Contacted by the BBC, a party spokesperson dismissed the remarks at the meeting as a "joke".
Greek police spokesman Lt Col Christos Manouras told the BBC on Monday that as soon as police heard the BBC broadcast, they recorded the clip of the Golden Dawn meeting and sent it to the office investigating the alleged attack on Mr Stratoulis.
The MP from the Syriza bloc was reportedly attacked after a football match in the Olympic Stadium on 16 December by three men who, he says, threatened to kill him. He is said to have suffered light injuries.
Golden Dawn is one of the most right-wing parties in Europe and its anti-immigrant language and logo, redolent of a swastika, underline why many call it neo-Nazi, the BBC's Tim Franks reports from Athens.
A recent opinion poll suggests the party's support has grown since the last election, when it won 18 seats in parliament.
Golden Dawn denies involvement in violence.
Leicester have been fined £20,000 by the Football Association over the conduct of their players during a game against Aston Villa.
[NEXT_CONCEPT]
Plans to rebuild the main stand at Tynecastle football stadium have been approved by Edinburgh city council.
[NEXT_CONCEPT]
Police in Greece have submitted a BBC tape to prosecutors investigating an alleged assault on an MP by members of the far-right Golden Dawn party.