Albert is being treated by doctors from the Princess Grace Hospital and the palace says they are not concerned for his health, despite the prince being in the at-risk age group.
The palace says the prince is working from home and remains in constant contact with members of the government.
Albert, the second child of movie star Grace Kelly, who married Prince Ranier III.
Just two days ago, Albert announced a ban on group gatherings and limited travel to healthcare and food shopping. The Monaco Grand Prix has also been postponed.
“The way out of this health crisis will depend on your ability to comply with the measures applied,” he told the public.
To date, there are 7 cases of the virus in Monaco, with 1 hospitalised.