According to John, Queen struck Linley, the son of her sister Princess Margaret, after he ignored her request to check in on his sister, Lady Sarah Armstrong-Jones, who she became ill during the event.
The singer wrote, "When [Linley] repeatedly tried to fob her off, the Queen lightly slapped him across the face, saying 'Don't' -- slap -- 'argue' -- slap -- 'with' -- slap --'me' -- slap -- 'I' -- slap -- 'am' -- slap -- 'THE QUEEN!'"
John claimed the monarch noticed he had witnessed the encounter, gave him a wink and walked away.
"I know the Queen's public image isn't exactly one of wild frivolity, but ... in private she could be hilarious," he said in the book.
John, who was knighted in 1999, is known for his close relationship with several royals, specifically Princess Diana, who died in August 1997 in a car crash in Paris. The 11-time Grammy winner sang "Candle in the Wind" at her funeral and has remained friends with her sons Prince William and Prince Harry.
In his memoir, John described Diana as someone who was "blessed with incredibly social ease, an ability to make people feel totally comfortable in her company." A quality, the musician said, she passed down to her children, William and Harry.