Mr Key recovered enough to look around "and very graciously left".
Ms Plummer later texted Antarctica NZ chief executive Lou Sanson to ask how Mr Key was faring. She received a reply thanking her for her concern and the way the restaurant handled the situation.
Mr Sanson advised her Mr Key was possibly suffering from jetlag.
But a spokeswoman for the Prime Minister later said jetlag was not a factor in the incident.
Mr Key returned from his summer holiday in Hawaii on Wednesday but the small time difference between there and New Zealand meant jetlag was unlikely.
The specialists that saw Mr Key couldn't specify a reason for his faint, "but sometimes these things happen", the spokeswoman said.
Mr Key had not had any health issues recently, "in fact, quite the opposite".
"He went through quite a rigorous health test for the Antarctic trip. He's in good health. The specialists saw no reason for any worries and cleared him to travel to Antarctica. They wouldn't do that given the lack of proximity to any major medical facilities if they weren't sure it was just a one-off."
Antarctica NZ administration team leader Joanne Avis said Mr Key passed his pre-visit medical. The medical included sinus, skull, throat, teeth, ear, skin, joints, spine and abdominal examinations, along with heart, lung, blood, urine, eyesight, hearing and even tuberculosis tests.
GP and former chairman of the Medical Association Peter Foley said fainting in an otherwise healthy person was generally a sign of fatigue or possibly dehydration.
"There's lots of causes of acute faint. This would probably be a result of overdoing it, changes in temperature and poor fluid intake. It's very common - blood pressure can drop when you haven't kept your fluids up for the day. Sometimes a glass of alcohol can dilate blood vessels and drop your blood pressure as well."
During his Antarctica visit, Mr Key will check New Zealand's territorial, scientific and commercial interests.