The 'Sex on Fire' group's drummer Nathan Followill thinks the 26-year-old royal - who is third in line to the British throne - is "cool" but his competitive nature came to the forefront when they recently met at London's The O2.
Nathan said: "We're still pretty wide-eyed about meeting dignitaries but he's the cool prince I think. He picked up a ping-pong bat backstage and we went at it.
"I'm not sure what the etiquette is when you play a prince at table tennis, but hey I'm the king aren't I? A king trumps a prince. I think the other guys thought, 'Maybe you should let a real prince win.'
"But he is so tall and he's got military training so I figured he can look after himself. It was a hard-fought battle but I took him in the end."
Nathan - who formed the band with his brothers Caleb, Jared and their cousin Matthew Followill, - also said while the group would be honoured if they were asked to play for Harry's brother Prince William's wedding in April, they would prefer to wait for the younger royal to get married.
He told The Sun newspaper: "Man, we would jump at playing the Royal Wedding if we were asked. Wills and Kate look like nice people.
"But Harry is the dude. His is the wedding we would most likely play. He knows his music. He keeps it real on his iPod."