Prince Charles, 71, is showing mild symptoms, “but otherwise remains in good health”, a spokesman said, adding the 72-year-old Duchess of Cornwall has been tested, but not the virus.
Charles and Camilla are now separating at Balmoral.
Buckingham Palace said the queen last saw her son, heir to the throne, on March 12, but was in “good health”.
Mahal said that the Duke of Edinburgh was not present at that meeting, and the queen was now “following all reasonable advice regarding her welfare”.
A statement from Clarence House wrote: “According to government and medical advice, the prince and duchess are now self-segregated at home in Scotland.
“The tests were carried out by the NHS in Aberdeenshire, where they met the necessary criteria for testing.
“It is not possible to find out which prince caught the virus during recent weeks due to high preoccupations in his public role.”
The Duke and Duchess arrived in Scotland on Sunday. Charles was exhibiting mild symptoms over the weekend and was tested by the NHS in Aberdeenshire on Monday.
The result came on Tuesday night, showing it was positive.
Charles is still working, up and about and in good spirits.
The 71-year-old heir to the throne last saw the queen on 12 March. Three days earlier, mother and son had more contact during Commonwealth Day service.
It is important to emphasize the Queen again in good health. He moved to Windsor last week with the Duke of Edinburgh who had come from his usual residence at Sandringham, Norfolk.
Given their ages, 93 and 98 respectively, special care will be taken not to endanger the virus.
Prince Charles and Camilla will follow government advice and vary. It is not a huge house, but certainly large enough to differentiate itself within it.
They’ve got a small staff with them – and it is expected that Charles will now stay in Scotland for a few weeks to recover from the symptoms.