A Clarence House spokesman said he was "displaying mild symptoms but otherwise remains in good health and has been working from home throughout the last few days as usual".
Prince Charles, 71, and the Duchess of Cornwall, 72, are now self-isolating at their home in Scotland.
The Duchess has also been tested for the virus but did not have it, the spokesman said.
The news comes as Boris Johnson faces MPs in the House of Commons for the final PMQs before an early recess.
Jeremy Corbyn used his first questions of Prime Minister's Questions to accuse Boris Johnson of being too slow to deal with the coronavirus pandemic.
Insisting that his last appearance as Labour leader did not signal his retirement, Mr Corbyn said care workers were being turned away from supermarkets running priority shopping hours.
"What is the Prime Minister's plan for making sure that care workers can get the vital food and supplies they need for the people that they're caring for?" he asked.
Experts confident NHS will be able to cope
Professor Neil Ferguson, who is recovering from Covid-19 himself, told the Science and Technology Committee measures taken by the Government could tip the outbreak from a growing epidemic to a declining epidemic.
The director of MRC Centre for Global Infectious Disease Analysis, Imperial College London, told the committee current predictions were that the NHS would be able to cope if strict measures continued to be followed.
He said: "There will be some areas that are extremely stressed but we are reasonably confident - which is all we can be at the current time - that at the national level we will be within capacity."
Drinking from a Keep Calm and Carry On mug, he explained: "There will be some resurgence of transmission but the hope is that by employing more focused policies to suppress those local outbreaks, we can maintain infection levels at low levels in the country as a whole indefinitely.
"It remains to be seen how we achieve this and how practical it proves to be."
Dutch sex workers told to down tools
Sex workers, driving instructors and masseurs have been ordered to stop work by the Dutch government as part of efforts to contain the coronavirus pandemic, reports James Crisp, Brussels Correspondent.
Amsterdam’s famous red light district, with its legal and regulated brothels, was shut on March 15 but escorts, who travel to meet clients, have been able to continue work.
Government advice published late on Tuesday said that the call girls had to stop working. Escorts are among the “contact professions” banned from working to prevent the spread of Covid-19. Others include masseurs and driving instructors, who cannot observe the 1.5 metre social distancing rules inside a car.
The government advice is meant to clarify and explain the measures announced on Monday. The Netherlands extended its ban on all public gatherings to June 1 from April 6.
The Dutch government has already ordered the closure of schools, bars, restaurants and gyms, as well as the country’s famous cannabis cafes and sex clubs.
‘Queen 'in good health'
Buckingham Palace has issued a statement about the Queen following the news that the Prince of Wales has coronavirus.
A spokeswoman said: "Her Majesty The Queen remains in good health. "The Queen last saw The Prince of Wales briefly after the investiture on the morning of 12th March and is following all the appropriate advice with regard to her welfare."
The Prince of Wales last saw the Queen for a private meeting on March 12, 13 days ago.
Their last public engagement together was at the Commonwealth Day service at Westminster Abbey on March 9.
The service also included the Duke and Duchess of Cambridge, the Duke and Duchess of Sussex, Boris Johnson and Carrie Symonds, Jeremy Corbyn and Dominic Raab.
The incubation period for coronavirus is generally about 5 or 6 days, but it can be as long as 14 days.
It is not yet known when the Prince of Wales first displayed symptoms.
Prince Charles met infected Prince Albert of Monaco on March 10 nine days before Albert announced he had the virus.
The pair met at a WaterAid event in London on March 10, where Prince Charles gave a speech.
Prince Charles' Covid-19 diagnosis makes him the most high-profile patient in the UK.
His press office today said the symptoms he is displaying are only mild, but the Prince of Wales comes into contact with a large number of people in his role as an active member of the royal household.
Clarence House said 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".
In the last two weeks, the Prince has given a speech at a dinner in aid of the Australian bushfires and at his own Prince's Trust award in London.
The World Health Organisation says the incubation period for Covid-19 can be as long as 14 days.