He stood “eyeball to eyeball” with Master of the Royal Household Tony Johnstone-Burt.
Brother Charles later asked him to apologise — but it wasn’t forthcoming.
Reports of the fracas, the talk of the Palace for weeks, emerged last weekend, without the identity of the staffer.
Pals say Andrew has been under “immense strain” for two months and “something snapped” that day.
It is still unclear what the disagreement was about or whether it involved the Duke’s relationship with disgraced billionaire Jeffrey Epstein, who took his life in prison last month.
An insider said of Andrew: “He just lost it. There was some talk a few months ago that Andrew was unhappy about moving out of his apartment during renovation work, but people are just speculating.
“They squared up to each other eyeball to eyeball.”
A friend of the Duke has said of the row: “There were heated words on both sides but it was in no way physical.
The friend added: “There was no apology because there was nothing to apologise for. The Duke maintains a good relationship with the Prince of Wales.”
As the Palace’s chief operating officer Johnstone-Burt is in charge of 250 staff and is overseeing the £369 million refurbishment.
He is a decorated naval veteran and, like Andrew, flew helicopters in the 1982 Falklands War.
A father-of-five with a ready smile, he is said to be a “favourite” of the Queen. A source said: “She loves him and likes his can-do attitude.”
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The Duke has been dogged by adverse publicity and unanswered questions about his friendship with paedophile Epstein, but vehemently denies any wrongdoing.
Asked if he was involved in an altercation Johnstone-Burt told The Sun: “Thank you but I’m afraid I can’t help at the moment.”
A Palace spokeswoman said: “Some time ago there was a disagreement between the Duke and a staff member. This was resolved.There are no ongoing issues.”
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