She had a fever and suffered from fatigue, according to a source close to the couple who spoke to The Sun.
According to the Sun, Princess Michael contracted the virus from a housekeeper who had mild symptoms.
Princess Michael has been in self-isolation at her home, Apartment 10 of Kensington Palace, with her husband. Her staff have been sent home to help prevent the spread.
Prince Michael, 78, has not tested positive for the virus and the princess has reportedly not had contact with the Queen recently.
The news follows Prince William's admission that he secretly battled coronavirus earlier this year, but kept the diagnosis a secret in the hope it wouldn't "alarm the nation".
According to reports the Duke of Cambridge contracted coronavirus in April and was "struggling to breathe" which created "panic" after he was knocked hard by the virus.
Prince William is believed to have suffered from Covid-19 days after Prince Charles and Prime Minister Boris Johnson also battled the virus.
In March Charles had the virus and had "mild symptoms" according to a Clarence House spokesperson.