Sarah Ferguson, who is divorced from the Queen's second son Prince Andrew, was due to be interviewed on a special edition of Michael Parkinson's programme on 24 November.
She was set to promote a charity which conducts research into babies' health.
Veteran interviewer Parkinson prides himself on adding journalistic rigour to his celebrity interviews, and it is likely he would have asked the duchess about the trial, which hit headlines worldwide.
A spokeswoman for the duchess said: "Even though this was purely a fundraising appearance on behalf of the Tommy's Building Blocks appeal, of which she was patron, she thought it was inappropriate to go ahead at this time."
A BBC spokeswoman told BBC News Online it "fully understood" her decision, adding: "We look forward to rescheduling the interview for a later date."
However, a newspaper claim that listings magazine Radio Times had to pull its print run halfway through, because its cover featured the duchess, was denied by its publisher, BBC Worldwide.
Inquiry
Mr Burrell's trial collapsed at the beginning of November, after it was revealed he had told the Queen he was keeping some of Diana's possessions.
He was found not guilty of three charges of stealing from the estate of Diana, Princess of Wales, the Prince of Wales and Prince William.
The trial is estimated to have cost at least £1.5m.
The internal inquiry, ordered by Prince Charles on 12 November, will look at concerns about the way the trial ended - when the Queen came forward with vital information - and the way an alleged rape was handled.
Official gifts
But the investigation will focus exclusively on the Prince of Wales's household and will not consider the Queen's role in the trial's collapse.
The inquiry is examining four key questions:
The investigation is being carried out by the Prince's private secretary, Sir Michael Peat, and defence barrister Edmund Lawson QC.
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