Barcelona defeated Real Madrid in extra-time 3-2, with Rudiger and Lucas Vazquez seeing red at the end of the final for protesting a decision made against Kylian Mbappe. Jude Bellingham also saw red for remonstrating with match officials.
Referee Ricardo de Burgos Bengoetxea said in his report that Rudige was dismissed for "throwing an object from the technical area, which missed me". The German is said to have lobbed an ice cube from the bench.
"There's definitely no excuse for my behaviour," Rudiger posted on an Instagram story. "I'm very sorry for that.
"Sorry again to the referee and to everyone I have disappointed."
There is a danger of a lengthy ban from the RFEF for Rudiger, which can range up to six months for "assault on referees", even if "the act was a single act and did not cause any harmful consequences".