Mr Guterres, 72, is isolating for the next few days and has cancelled in-person engagements, sources told AFP.
The UN chief was due to be the UN Press Association's guest of honour at its annual gala in Manhattan on Wednesday. On Thursday, he was to participate in a UN Security Council meeting on the challenges of terrorism and climate change, led by Niger's President Mohamed Bazoum.
Mr Bazoum, whose country holds the council presidency, arrived in New York on Tuesday and is expected to stay until the end of the week when he heads to Washington.
UN spokesman Stephane Dujarric declined to comment on Mr Guterres's condition.
Mr Dujarric indicated a few days ago that Mr Guterres had recently received his third dose of the Covid-19 vaccine. He hesitated about receiving the booster shot as millions of people around the world are yet to receive their first jab.