Prince Philip, a former naval officer infamous for his colourful off-hand remarks, was visiting cadets in Exeter, south-western England, when he put the question to Elizabeth Rendle.
The 24-year-old, who works as a barmaid in a nightclub, was asked what she did for a living.
"I just said that I worked in a club, and then he asked, 'Oh, what, a strip club?"', she told London's Daily Telegraph. "Obviously, I said, 'No', and then he said, 'Oh, it's a bit too cold today, anyway.'
"I was quite surprised but I think he was just trying to lighten the mood. It was a joke and we were all laughing, which drew everyone else's attention to us.
"I don't think he put his foot in it. It was a joke and I didn't take any offence. I think he was just putting people at their ease."
The Duke of Edinburgh's comments are usually intended to put the other person at ease when meeting royalty but have landed him in hot water on foreign visits.
Dontopedalogy (sic)is the science of opening your mouth and putting your foot in it, a science which I have practiced for a good many years. - Duke of Edinburgh Prince Philip (and it appears that after so many years of practice his highness has perfected the art of putting his foot in his mouth whenever he opens the latter!)