Charles is currently in isolation in Aberdeenshire, Scotland. Questions have been raised over why he was eligible for a test from NHS Grampian while many frontline medical workers have been unable to get them.
Catherine Calderwood said the prince had been tested for "clinical reasons", the BBC reported.
Clarence House announced on Wednesday that the Prince of Wales - who is known as the Duke of Rothesay in Scotland - had tested positive for the virus.
Clarence House said the couple "met the criteria required for testing", but the National Health Service Scotland website states that "generally" people are only tested if they have "a serious illness that requires admission to hospital", the report said.
The report noted that questions have also been raised about why the Prince was allowed to travel to Scotland after he had started to show mild symptoms.
People have been urged not to use second homes or holiday lets in remote parts of Scotland for self-isolation, as this can add extra pressure to local health services.
First Minister Nicola Sturgeon said she did not want to comment on the specific case of the Prince, but added: "We want people to behave responsibly, we don't want people to see the Highlands and islands of our country as places where they can outrun the virus.
"Obviously there are places where people have homes in Scotland and people will choose to go to their homes, but we should all be responsible."
Wednesday's Clarence House statement said that Prince Charles has been displaying "mild symptoms but otherwise remains in good health and has been working from home throughout the last few days as usual.” In keeping with social distancing advice during the pandemic, Charles has been noticeably using 'namaste' as a greeting rather than a handshake when seen in public over the last few weeks, including during an event to mark the Commonwealth Day on March 9 at Marlborough House in London.
His wife Camilla, 72, was seen wearing long black gloves during the same event.