OTTAWA—Canadian Prime Minister Justin Trudeau on Thursday said he would isolate himself for a 14-day period after his wife, Sophie Grégoire Trudeau, tested positive for the new coronavirus.

A statement from Mr. Trudeau’s office, issued late Thursday, said the prime minister is in good health and wouldn’t be tested for the virus at this stage because he hasn’t experienced symptoms. Doctors said there is no risk to those who have had recent contact with Mr. Trudeau because he hasn’t had symptoms, the prime minister’s office...