A number of players from both teams were involved in a fracas in injury-time of the Premier League fixture at the King Power Stadium following a poor tackle by Leicester's Matty James on Villa defender Jores Okore.
Referee Michael Oliver showed James a straight red card for his challenge, and Villa's Ciaran Clark was then handed a second yellow for confronting the Leicester midfielder.
A melee involving numerous players ensued and the FA announced on Tuesday that the Midlands clubs have both been charged.
"It is alleged that during added time at the end of the second half, both clubs failed to ensure their players conducted themselves in an orderly fashion and/or restrained from provocative behaviour," an FA statement read.
"The clubs have until 6pm on 16 January 2015 to respond to the charge."
Paul Konchesky's first-half goal gave bottom-placed Leicester a 1-0 victory over Villa, who have now gone six Premier League games without a win.
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
