Secretary General Antonio Guterres was in his office on Monday, according to Dujarric.
The UN Security Council's Chinese presidency cancelled Monday the body's two final meetings scheduled this week due to the coronavirus crisis, diplomatic sources said.
After the earlier cancellation of the meeting planned for Tuesday, the Security Council was planning to discuss the situation of Darfur in Sudan on Wednesday, and address multilateralism on Thursday.
It was not possible Monday to confirm the cancellations with the Chinese mission to the United Nations, which currently holds the rotating presidency of the Security Council.
Diplomats from other countries however confirmed the decision.
UN spokesman Stephane Dujarric told journalists that a positive Covid-19 case had been identified among staff at the UN secretariat, after a Philippines diplomat was reported infected last week.
The United Nations building remains open and Secretary General Antonio Guterres was in his office on Monday, according to Dujarric.
But the number of people entering the building in New York city has shrunk: only some 900 people, rather than the normal several thousand per day, he said.
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