The FA has charged Aston Villa and Leicester City for failing to control their players.
Both clubs now have until Friday to respond to the charge and will likely face large fines as punishment from the governing body.
"Both Aston Villa and Leicester City have been charged by the FA following their fixture on 10 January 2015,” an FA statement said.
"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 refrained from provocative behavior.”
The brawl came at the end of the game, which Leicester won 1-0, when City midfielder James went in hard on Villa defender Jores Okore. That tackle produced an angry response from Clark, who berated the midfielder for the tackle.
That sparked a confrontation, which saw most of the players on the pitch clashing in the centre circle. The pair later saw red for their actions, and consequently clashed in the tunnel, requiring stewards and coaching staff to to separate them.
They could also face retrospective fines from the FA, although that remains unlikely given the referees decision to award both players red cards during the game.