The Newsroom star related the tale to Life & Style after being asked about her most embarrassing moment.
"I'm friends with [Obama's former aide] Reggie Love and I was at the White House," Munn explained. "I looked up and realised I was in the Oval Office.
"Of course, I'm texting because that's what I'm always doing. I am texting somebody and I look up and I see Obama and I look back down - it's not registering that it's him. I totally gave him the brush-off, like, 'Oh hey, what's up, Obama?'"
Munn continued: "I had to do a double-take, like, 'Oh my God, I am so sorry'. It was so embarrassing. I was like, 'I don't want you to think that I was the girl that was like uhhh'."
Munn, who is thought to be dating The Killing's Joel Kinnaman, recently joked that she visited the Magic Mike set on her days off to "rate" the male stars.