Walker and Stevenson were embroiled in a scuffle towards the end of the ill-tempered match, which Hearts won 2-1.
However, neither player was punished by the referee at the time of the incident.
Stevenson has been charged with serious foul play, while Walker's charge is for violent conduct. The duo could be banned for two matches if they accept their respective charges.
Both players have until 3pm on Wednesday to respond to the charges.