The asteroid, 2014 RC, will pass over New Zealand at around 18:18 GMT. It is about 60 ft (18 m) in size.
It will be about 40,000 km (25,000 miles) away, posing no danger to Earth, Nasa said.
While it will be too small at that distance to see with the naked eye, amateur astronomers with telescopes may glimpse it as it passes, Nasa added.
The asteroid was first discovered on 31 August, and, at its closest approach, will be about one-tenth of the distance from the centre of the Earth to the moon, Nasa said in a statement.
It is expected to orbit near Earth again in the future.
In February 2013, a meteorite of a similar size exploded over Chelyabinsk in Central Russia, injuring more than 1,000 people.
Nasa currently tracks more than 11,000 asteroids in orbits that pass relatively close to Earth.