ALBANY, N.Y.—The executive director of the Port Authority of New York and New Jersey has tested positive for the novel coronavirus, as the state of New York surpassed Washington state with the most cases in the country, New York Gov. Andrew Cuomo said.

Rick Cotton, the Port Authority head, is presently working from home, and members of his senior team are being tested, Mr. Cuomo said at a news conference Monday morning. The governor didn’t say how Mr. Cotton contracted the virus. The Port Authority oversees the airports in...