The 62-year-old's COVID-19 diagnosis was revealed on March 19 by the Prince's Palace. The day before, the royal said Monaco would go into lockdown to fight the virus, which the World Health Organization has declared a pandemic.
In a statement, the Palace said Albert, who is married to Princess Charlene and is the son of the late Princess Grace, continues to work from home and is in a good state of health. He will be monitored by his doctor and specialists from the Centre Hospitalier Princesse Grace, but is not in hospital.
Earlier this week, Serge Telle, Monaco's prime minister, tested positive for the coronavirus.
On March 17, Albert addressed Monaco in a speech in which he announced the plans for the city-state to go in to lockdown.
"The way out of this health crisis will depend on your ability to comply with the measures applied," he said.
Earlier this week, Karl von Habsburg, the ancestral Archduke of Austria, also tested positive for coronavirus. The 59-year-old told oe24 that COVID-19 is "annoying" but said he's "fine."
"It's not the Black Plague," he said. "I thought it was the usual flu. When a friend called me that he had a positive test at a congress in Switzerland, I was also tested."
Karl said he's been listening to health advice, doing everything his doctors ask and isn't panicking.
Coronavirus has already affected many royal families. Spain's King Felipe VI and Queen Letizia were tested last week after Letizia met with a government minister who later came down with the illness. Both the King and Queen were found to be negative.
In the UK, the Queen and Prince Philip have both been moved to Windsor Castle, where they will begin an early Easter break. A number of events have been cancelled in the Queen's schedule, including Maundy Thursday service at St. George's Chapel on April 9, the Garden Parties she traditionally hosts each year, and the state visit by Japan's Emperor Naruhito and Empress Masako.
Princess Beatrice and Edoardo Mapelli Mozzi have cancelled their wedding reception, which was to take place at Buckingham Palace following their ceremony on May 29. They are still scheduled to wed that day, but are exploring having a private ceremony that involves close friends and family.