"As of now, we have not been advised of any COVID-19 cases amongst UN staff in New York," UN spokesman Stephane Dujarric said in a statement.
Some 3,000 people work in the iconic building overlooking the East River in Midtown Manhattan, the scene of annual gatherings of world leaders.
Normally, some 5,000 tourists visit the building each week in guided tours.
About 500,000 people visit the UN headquarters each year, not all tourists, officials said. "The United Nations will continue to monitor the situation closely and further measures may be taken as circumstances evolve," Dujarric said.