Prince Charles, 71, is displaying mild symptoms “but otherwise remains in good health”, a spokesman said, adding that the Duchess of Cornwall, 72, has been tested but does not have the virus.
Charles and Camilla are now self-isolating at Balmoral.
Buckingham Palace said the Queen last saw her son, the heir to the throne, on 12 March, but was “in good health”.
The palace added that the Duke of Edinburgh was not present at that meeting, and that the Queen was now “following all the appropriate advice with regard to her welfare”.
A Clarence House statement read: “In accordance with government and medical advice, the prince and the duchess are now self-isolating at home in Scotland.
“The tests were carried out by the NHS in Aberdeenshire, where they met the criteria required for testing.
“It is not possible to ascertain from whom the prince caught the virus owing to the high number of engagements he carried out in his public role during recent weeks.”