A number of players from both teams wrestled and squared up during an angry confrontation following a challenge by Aberdeen's Dominic Ball on the Hearts midfielder Sean Clare during the hosts' 2-1 win.
Referee John Beaton cautioned Ball and Lewis Ferguson from the visitors, plus John Souttar and Arnaud Djoum from the home side at the time. However, the SFA have stepped in to punish both clubs for the on-field exchange.
Hearts and Aberdeen both stand accused of breaching SFA disciplinary rule 204: Where three or more players and/or members of team staff from one team are involved in a confrontation with opposing players and/or members of team staff of the opposing team during and/or directly after a match.
They must respond to the charge by Wednesday, April 10, with a principal hearing date set for Thursday, April 25.
The SFA have also moved to punish Rangers, Celtic, Scott Brown and Steven Gerrard for their conduct during Sunday's match at Celtic Park. The two Glasgow clubs are allegedly in breach of the same rule as Hearts and Aberdeen in relation to on-field altercations between their players.
Brown has been cited for acting in an improper manager, while Gerrard stands accused of misconduct during the match, which Celtic won 2-1.