The cyclone earlier caused flooding and landslips in Samoa and American Samoa.
The category one cyclone intensified on Sunday as it slowly moved at about 17 km/h through Tonga's northern waters and was predicted to pass within 60 km of Niue overnight, with the island's meteorology department saying there was a chance it could veer off course and hit the country directly.
The chief of police, Tony Edwards, said authorities weren't taking any chances and had issued a "yellow alert" advising residents to prepare themselves on Sunday afternoon.
"So if they could batten up their houses, make sure that they've got enough welfare for them, and the other thing is because we're going into the nightfall we don't want anyone running around at night," he said. "We can't determine what's going to happen, but we're going to ensure that our people are prepared for the worst."
Edwards said he had spent the afternoon canvassing the island and people appeared to be heeding the message to be prepared before nightfall, with many residents boarding up windows and securing loose items.
He said the National Disaster Committee was meeting regularly and would monitor the situation through the night, with strong winds and heavy rain forecast.
Misaeli Funaki, a forecaster at the Fiji Meteorological Service which is responsible for tracking and naming cyclones in the southwestern Pacific, said that despite only being a category one, the cyclone would pass very close to Niue and could cause severe damage.
"It'll pass by just due east of it, but [with] the associated weather, we're saying sustained winds of 35 knots or even more, and as the system moves in closer we expect the observed winds to increase for Niue," he said.
"But even as just a category one system it can be devastating or very damaging for Niue."
In a tropical cyclone advisory issued on Sunday evening, forecasters warned that damaging gale force winds of at least 75 km/h would begin several hours before the cyclone's centre passed overhead or nearby the country.