Albert, 62, appeared to be the first head of state who has publicly said he contracted the virus.
In a statement Thursday, the palace said he is being treated by doctors from the Princess Grace Hospital, named after his U.S. actress mother.
It added that Albert is continuing to work from his home office in the palace and is in constant contact with members of his government.
In the statement, Albert urged residents of his tiny Mediterranean principality to respect confinement measures.
Albert is the second child of Princess Grace — formerly Grace Kelly — and Prince Rainier of Monaco.
He became a five-time Olympic bobsledder and in recent years has been a global environmental campaigner.
Fluent in English and French, Albert graduated from Amherst College in Massachusetts with a degree in political science in 1981, and is a member of the International Olympic Committee.
He and his wife, the former Charlene Wittstock, have twin children.