The Duke of Edinburgh's question provoked howls of laughter from Elizabeth Rendle, 24, and her friends, reports the Daily Mail.
Miss Rendle, a barmaid, said Philip had asked her what she did for a living: "I told him I worked in a club. He then asked if it was a strip club," she said.
The 88-year-old royal then appeared to think better of the suggestion in the current weather and joked that such an occupation would be "too cold".
The Duke was with the Queen at Wyvern Barracks in Exeter during a tour of Devon.
Miss Rendle later said that, far from being offended by the question, she felt Prince Philip had been "putting people at their ease".
She said: "He was just going round chatting with people, asking them what they did for a living.
"It was a joke and we were all laughing which drew everyone else's attention. I don't think he put his foot in it. It was a joke and I didn't take any offence."
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