The aviation code to warn pilots flying over the area was raised to orange in August, but has since dropped to yellow.
GNS Science duty seismologist John Ristau said the quake was unrelated to volcanic activity.
"Typically these earthquakes are actually not directly related to the volcano - they're not really volcanic earthquakes, they're not indicative of any volcanic activity."
He said earthquakes of a similar size around White Island were not really unusual.
"You get these ones that are between magnitude 3 and 4 size earthquakes - there's nothing really unusual about those."
Dr Ristau said people tended not to feel quakes near White Island on the mainland.
"Because they're a little way offshore, people tend to not really feel them."