"I'm really happy with the silver medal. Of course, my goal was to win gold, but if you would have asked me yesterday, I would have named Kristin [Armstrong] as favourite for today," Arndt said, according to shewired.com.
Armstrong, an American, won gold in the event, while Russian Olga Zabelinskaya took bronze.
Arndt, who is one of at least 23 openly gay athletes at the Summer Games, is competing in her fifth Olympics.
The German now turns her focus to the team pursuit event today.