Clarence House announced that the 71-year-old heir to the throne was displaying mild symptoms "but otherwise remains in good health," a spokesman said, noting that the Duchess of Cornwall, 72, had been tested but did 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, and he was in good health.
The palace affirmed that the Duke of Edinburgh was not present at that meeting, and that the Queen was now "following all appropriate advice with regard to her welfare."
Clarence House said that 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 National Health Service (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."
Meanwhile, a quarter of the world’s population began living under some form of lockdown yesterday, including restrictions on gatherings and travel outside the home. How strongly this was enforced and policed varies across countries.
This came after India, a country of some 1.3 billion people, spent its first day in lockdown.
Spain recorded its biggest daily increase in fatalities, bringing its total death toll to 3,434 - surpassing China and putting it second only to Italy. Global cases exceed 400,000 with deaths approaching 20,000 and more than 100,000 recovered.
In Latin America, Colombia began a period of “mandatory preventive isolation” yesterday, meaning people all over the country will have to stay in their homes. Exceptions include medical appointments, shopping for essential goods like food, medicine and cleaning products, and going to the bank.
Paraguay became the latest Latin American country to close its borders. The government announced on Tuesday that they would remain sealed until Sunday following a second death in the country from coronavirus.
Mexico called on businesses to stop employment that involves the movement of people from their homes to their workplaces. The country has entered the second stage of coronavirus transmission, meaning it has detected a case that has been passed from person to person locally, rather than coming from abroad.
Brazil’s president Jair Bolsonaro criticised the media for "fear-mongering" and has called on mayors and governors to roll back restrictions they have introduced to curb the spread. Bolsonaro stated that people aged over 60 were at risk, but most people - including himself - had nothing to fear. Over 2,200 cases of the virus have been reported in the country. The president has been accused of having a cavalier attitude to the pandemic.