The monarch "politely but firmly" declined the award, but sent a message with her "warmest best wishes".
Author and broadcaster Gyles Brandreth, chairman of the awards, wrote to the Queen's private secretary, Sir Edward Young, to ask if she would accept the main Oldie of the Year accolade.
But in a letter published in the November issue of the magazine, her assistant private secretary, Tom Laing-Baker, wrote: "Her Majesty believes you are as old as you feel, as such The Queen does not believe she meets the relevant criteria to be able to accept, and hopes you will find a more worthy recipient."
The Queen, who is just five years away from her 100th birthday, is the nation's longest reigning monarch and is due to celebrate her Platinum Jubilee - 70 years on the throne - next year.
She still keeps a busy diary of events and audiences and deals with her daily red boxes of official papers.
She held two audiences on Tuesday via video link from Windsor Castle, and will later host a reception at Windsor for international business and investment leaders to mark the Global Investment Summit.
For the past 29 years, the Oldie of The Year Awards have celebrated the achievements of those of the older generation who have made a special contribution to public life.
Previous winners have included everyone from Oscar winners to Nobel laureates, from community care nurses to veteran athletes, from Sir John Major to Dame Olivia de Havilland and David Hockney.
Brandreth revealed that actress Dame Maureen Lipman, one of the judges, raised the prospect of the magazine honouring the Queen in recognition of her leadership during the pandemic and ahead of the Jubilee.
He described the letter he received from Balmoral Castle in response as "lovely", writing: "Perhaps in the future we will sound out Her Majesty once more."
The late Duke of Edinburgh, who passed away in April this year, was named Oldie of the Year in 2011 to mark his 90th birthday.
The monarch has been pictured out and about at the Royal Windsor Horse Show and Ascot in recent months, and still enjoys riding her own ponies.
Last week, she used a walking stick for what is believed to be the first time at a major public event when she attended a service marking the centenary of the Royal British Legion.