The Prince of Wales is only displaying mild symptoms and is otherwise in good health, Clarence House said in a statement. It is unknown how the 71-year-old caught the virus because of his recent busy schedule of public events.
The Queen, 93, remains in "good health" and is "following all the appropriate advice with regard to her welfare," a Buckingham Palace spokesperson said Wednesday.
It is unclear why Prince Charles was advised he was not contagious earlier. The coronavirus incubation period -- the amount of time from exposure to symptoms -- is usually around five or six days, with a maximum of around 12 days, according to research published this month in the medical journal Annals of Internal Medicine.
According to a royal source, Prince Charles started showing symptoms last weekend, meaning he could have been exposed before he saw the Queen on March 12.
He was tested on Monday and received the results on Tuesday, the source told CNN.
Prince Charles's office at Clarence House has not responded to CNN's query regarding the timeline. "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," his office said earlier.
Both Public Health England and the US Centers for Disease Control and Prevention say there are indications people could be contagious before they show symptoms. While people are probably most contagious when they are symptomatic, scientists currently cannot pinpoint exactly when people can start spreading the disease.
Following his last public event on March 12, Prince Charles has had a number of private meetings with individuals, all of whom have been made aware of the situation.
The tests were carried out by the National Health Service in Aberdeenshire, where the couple met the criteria required to be tested, the statement added.
Prince Charles has not been to hospital, the royal source said Wednesday, adding that he was tested because of his age and medical history. He has spoken to the Queen and to his sons William and Harry, the source said. The medical advice he has been given is that this is "unlikely to escalate into a more serious case."
Prince Charles continues work and is in "good health and indeed good spirits," the royal source told CNN.
The prince has a reputation for working hard, and meets more members of the public than virtually any other member of the royal family. His aides are now racing to determine how, when and where he contracted the virus, and with whom he may have had contact since.
Despite the Queen being in her mid-90s, it is not known whether she has been tested.
The source asked not to be named discussing the royal family's medical condition.
In a statement issued by the palace as they moved to Windsor, the Queen said the world was entering "a period of great concern and uncertainty" and warned that many would need to "find new ways of staying in touch with each other and making sure that loved ones are safe." She said she and her family were ready to play their part.
Prince Charles is the eldest child of the Queen and Prince Philip, the Duke of Edinburgh. As someone over 70, he is considered to be at higher risk than average for coronavirus.
Earlier this month, his office said he was not yet self-isolating because UK government and medical advice at the time were not advising over-70s to do so.
On March 13, Prince Charles and his wife announced they were canceling their spring tour due to the escalating coronavirus pandemic. The pair had been set to visit Bosnia and Herzegovina, Cyprus and Jordan.
CNN Health's Arman Azad contributed to this report.