The Queen is under medical supervision at Balmoral Castle.
Meghan and Harry were due to attend the WellChild Awards ceremony in London on Thursday evening, but have changed their plans to travel to see the Queen.
A spokesperson for the couple said: “The Duke and Duchess of Sussex will be travelling to Scotland."
Prince Charles, Camilla, Duchess of Cornwall and Princess Anne have travelled to Her Majesty's Highlands estate.
Prince William, Prince Andrew, Prince Edward and Sophie, Countess of Wessex, are on their way.
Kate, Duchess of Cambridge has remained in Windsor as Prince George, Princess Charlotte and Prince Louis are on their first full day at their new school.
A statement from Buckingham Palace reads: “Following further evaluation this morning, The Queen’s doctors are concerned for Her Majesty’s health and have recommended she remain under medical supervision.
"The Queen remains comfortable and at Balmoral.”
The monarch has had ongoing mobility issues and looked bright but frail and used a walking stick during Tuesday’s historic audience with Prime Minister Liz Truss.
That meeting followed a visit from outgoing Prime Minister Boris Johnson as he tendered his resignation.
During her Platinum Jubilee celebrations, she only travelled to Buckingham Palace twice, first for her Trooping the Colour balcony appearance and then for a finale after the pageant.
She secretly spent a night in hospital in October undergoing tests and was then under doctors’ orders to rest for the next three months, missing the Remembrance Sunday Cenotaph service and Cop26 climate change talks.
The Queen caught Covid-19 in February, and suffered from mild cold-like symptoms but said the virus left her “very tired and exhausted”.
The Prime Minister said: "The whole country will be deeply concerned by the news from Buckingham Palace this lunchtime.
"My thoughts – and the thoughts of people across our United Kingdom – are with Her Majesty The Queen and her family at this time."
Meghan Markle and Prince Harry
MOLLY DARLINGTON
The Queen with Prime Minister Liz Truss this week
Jane Barlow