The disgraced duke - at the centre of a storm over “ridiculous” plans to fly the Union Jack over town halls for his birthday - agreed to turn down the senior role for the sake of the Queen.
Her Majesty was due to promote her favourite son ahead of his 60th birthday later this month.
But the prince will turn down the move in a bid to protect the Queen from any further backlash over the Epstein sex trafficking scandal, the Express reports.
It is longstanding standard practice to treat senior Royals as if they had stayed in the Armed Forces and as a result promote them.
Prince Andrew stepped back from royal duties last year after a TV interview over his friendship with paedophile Jeffrey Epstein.
He also faces claims -which he denies -that he forced teenager Virginia Roberts to have sex.
A Buckingham Palace spokeswoman said: “By convention, the Duke of York would be in line for military promotion on his 60th birthday.
“Following the decision by His Royal Highness to step back from public duties for the foreseeable future, the Duke of York has asked the Ministry of Defence if this promotion might be deferred until such time that His Royal Highness returns to public duty.”
It comes as critics accused officials of “putting stuffy history in front of public opinion” over the birthday flag plans.
An email was sent to councils by civil servant Matt Stevenson -private secretary to Whitehall bigwig Dame Melanie Dawes -reminding them to fly the flag for the Prince on February 19.
Deputy Labour leadership candidate Ian Murray said: “This protocol has to be binned given the allegations against the Prince.”
MP Wes Streeting added: “This would be wholly inappropriate. It should be knocked on the head immediately.”
A council source ranted: “Making this gesture while there is a cloud hanging over the Duke is hugely insulting to Epstein’s victims and those wanting answers.”
Andrew left the Navy in 2001 to become a full-time working royal.
Eldest brother, Prince Charles, was made an Admiral at the age of 58 and his sister Princess Anne was given the same honour at 62.
But palace and defence officials suggested the promotion could be awarded later if he clears his name.
The latest humiliation for Andrew, which follows the cancellation of a planned birthday reception, comes amid frustration from US authorities, who have allegedly tried in vain to arrange an interview with him.
A lawyer for Epstein's victims claims she has a NEW witness who saw Prince Andrew dancing with Virginia Roberts at the Tramp nightclub.
Lisa Bloom said the woman had been partying with a friend when she accidentally stepped on a fellow reveller's toes at the exclusive nightspot in London in 2001 - before realising it was the royal.
And the witness claimed she saw the prince with a young woman - since recognising her as a young Virginia Roberts, who claims she had sex with Andrew when she was a teen.
Prince Andrew has denied the allegations, stating he has "no recollection" of meeting Ms Roberts and was instead at a Pizza Express in Woking for a party on the night in question.
Lawyer Ms Bloom said she had been approached by the witness after Prince Andrew's interview with Newsnight.
She said: "Her story is this - she was there in the nightclub and she stepped on the foot of somebody who was dancing next to her.
"She said 'I'm sorry', he said 'that's OK'."
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