'No excuse': Real Madrid's Rudiger after throwing object at ref
The centre-back was substituted in extra-time and in the final stages of Barcelona's 3-2 Clasico victory, threw something at referee Ricardo de Burgos Bengoetxea in protest.
Rudiger, who had to be held back from confronting the official by team-mates and staff, was shown a red card, with team-mates Lucas Vazquez and Jude Bellingham also dismissed at the end of the game.
"There's definitely no excuse for my behaviour last night. I'm very sorry for that," said Rudiger in a post on Instagram.
"Before the final whistle I did a mistake. Sorry again to the referee and to everyone I have disappointed last night."
Rudiger could face a ban of between four and 12 matches for his actions, which could see him miss the upcoming La Liga Clasico on May 11.
Vazquez and Bellingham's red cards are likely to lead to bans in next season's Copa del Rey for being less serious infringements of the rules.
Before the final the two main referees complained about attacks from Real Madrid's club television channel against officials this season.
De Burgos Bengoetxea broke down in tears as he spoke about the impact on his family life of Real Madrid TV's criticism.
Los Blancos responded furiously, pulling out of pre-match commitments on Friday and labelling the officials' comments "unacceptable".
Barcelona have beaten Real Madrid in all three Clasicos this season, with Los Blancos' last chance of major silverware the league title, where they trail their rivals by four points.