The American Idol and X Factor judge told The Tonight Show with Jay Leno that the Queen had snubbed him when they met in December 2007.
Cowell said: "It was actually embarrassing. It is called the Royal Variety Show, so she is in the audience.
"At the end, if you are involved in it, you have to stand around for hours and then say 'hello'. She ignored me and her husband called me a sponger.
"I think he was trying to be rude. So I just mumbled something and he walked off."
A Palace spokesman told the Daily Mail: "The Duke of Edinburgh categorically did not call Mr Cowell a sponger. He has no reason to.
"He has said he does not know enough about Mr Cowell to make any sort of comment about him. Mr. Cowell may have misheard the Duke, he has a very soft voice."
The Palace added: "The Queen doesn't ignore people. She has many people to meet after such a show."
