But despite being constantly spun around by her partner, Alexander Gamelin, Ms Min handled the mishap like a pro.
Instead of stopping and sacrificing points, the 22-year-old opted to continue the dance.
And, after a few mid-routine adjustments to the garment, the pair managed to complete their programme and finish ninth.
Following the competition, she told the Detroit Free Press: “Five seconds into the routine, my hook came undone. I was like, ‘Oh no!’
“If that comes undone, the whole thing could just pop off. I was terrified the entire programme.
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“This is my first Olympics, our first program and if my top were to come down, that would have been a disaster.
“I was very nervous that the entire thing was going to come off.”
Ms Min was born in California to South Korean parents and holds dual citizenship.
She chose to compete for her parents’ home country, and her partner, Mr Gamelin became a South Korean citizen so he could compete alongside her.
Ms Min managed to see the funny side and joked she would “sew herself in” for her next event.
She tweeted: “Despite the wardrobe malfunction, I had an amazing time competing in my home country!
“I promise to sew myself in for the individual event.
“I would like to thank the audience for keeping us going until the end. Couldn’t have done it without you guys.”
Last week she told The Boston Globe she and her partner were at the Winter games for the experience, not the top prize.
She said: “We’re not going for a medal or anything, so there’s not that much pressure on us.
“We just want to have fun.”