The "Homeland" star met Beyonce backstage at the 2016 Council of Fashion Designers of America (CFDA) Awards, where Claire was serving as a guest presenter, and the "Formation" hitmaker was receiving the Fashion Icon honour.
The two ladies shared a few moments by the side of the stage as they waited for their cues, and ended up making small talk.
"Oh, I got stupid in front of Beyonce," she confessed to Mastermind magazine. "We were backstage at, I think, the CFDA Awards. I was about to present. She was going on after me or something, so we had this kind of awkward minute while we waited. She was bedazzled and had a huge hat on - exactly the version of Beyonce you'd want to meet."
Claire recalls desperately trying to keep her cool as the conversation progressed.
"I think she said, 'I'm a big fan.' And I was like, 'Well, Beyonce, I, too, am a big fan,' " Danes remembered. "She was like, 'My husband and I watch your show (Homeland).' And I was like, 'That's amazing. Thank you! What are you working on now?' And she was like, 'I've been on tour but I'm finally going to be done soon and we're going to go on holiday.' "
However, the actress then made the mistake of inquiring about Beyonce and husband Jay-Z's family travel plans - and that's when she knew she had made a fool of herself.
"I was like, 'Where, Beyonce?' And she said, 'Yeah, I don't know. I'm still thinking about it,' " Claire said.
"I was such an idiot. Obviously you do not ask Beyonce where she's going on her holiday. You don't do that. So I panicked and tried to find a crack in the floor I could slip through."