Admiral Sir Timothy Laurence, the husband of the Princess Royal, has tested positive for coronavirus.
A royal source said Anne and her husband will now not be spending Christmas with the Queen as they will be isolating.
Earlier this week, it was revealed the Queen would be spending her first Christmas without her husband, Prince Philip – who died in April – at Windsor Castle.
The monarch usually hosts her family at Sandringham in Norfolk, with crowds of wellwishers turning out to watch the royals walk to the Christmas Day service at St Mary Magdalene Church on the estate.
It is not yet known where the Prince of Wales, the Duchess of Cornwall and Duke and Duchess of Cambridge will be spending Christmas.
Last week, it was revealed the Queen had cancelled plans for her pre-Christmas family lunch, due to be held on Tuesday.
The annual event allows members of the family who cannot travel to Sandringham to spend time with the monarch, but last year’s lunch was also cancelled because of the pandemic.
The Queen also spent last Christmas at Windsor, where she and the Duke of Edinburgh stayed shielded throughout lockdowns.
Christmas celebrations for the royals were previously always held at Windsor, but moved to Sandringham in 1988 when the castle was being rewired.
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