Under Spanish Football Federation rules, Rudiger could be suspended between four and 12 matches for "throwing an object" at referee Ricardo de Burgos Bengoetxea, who broke down in tears at a press conference on Friday while blaming constant pressure from Real Madrid television.
The suspension will leave Rudiger unavailable for the next few La Liga matches as Real sit four points behind leaders Barça, who they face on May 11th in a decisive game in the title race.
Bellingham and Lucas Vazquez, who were also sent off for vehement protests while on the bench in extra time, risk a less severe sanction that will not affect the end of their season.
England midfielder Bellingham was shown a red card for showing "aggressive behaviour" towards the referee and even had to be "restrained by his teammates" as he tried to enter the pitch.
"I don't want to talk about the referee. I don't know what happened at the end of the match," reacted Madrid coach Carlo Ancelotti, who was shown a yellow card for indiscipline.
The final was played against a tense backdrop following Friday's statements by the two main referees, who denounced constant pressure from Real Madrid TV and announced a collective response to the waves of harassment they face.
The comments have provoked fury from the Madrid giants, who have been engaged since February last year in an institutional war against a refereeing system they consider "completely discredited" and "corrupt from within" following decisions that have gone against them in La Liga.