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Charles, eldest son of Queen Elizabeth, is displaying what Clarence House said were mild symptoms, but the 71-year-old remains in good health and has been working from his home on the Balmoral Estate in Scotland.
His wife, Camilla (72), tested negative.
"The Prince of Wales has tested positive for coronavirus," Clarence House said on Wednesday.
"He has been displaying mild symptoms but otherwise remains in good health and has been working from home throughout the last few days as usual."
"The Duchess of Cornwall has also been tested but does not have the virus," Clarence House said.
A royal source said the Prince of Wales was tested on Monday and got the results on Tuesday. Charles has spoken to the Queen and his children, Prince William and Prince Harry.
Charles last saw the 93-year-old monarch on the morning of March 12 following an investiture, before the earliest time he would have been infectious.
"Her Majesty The Queen remains in good health," Buckingham Palace said.
"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.”
A royal source said that the earliest Charles would have been infectious was March 13.
The Queen left London for Windsor Castle on March 19. She is with her 98-year-old husband Philip, the Duke of Edinburgh.
"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," Clarence House said.
Britain is in its second day of lockdown. On Tuesday, the number of deaths from Covid-19 jumped 87 to a total of 422 - the biggest daily increase since the crisis began.