The plane was carrying parachutists heading for a tandem skydive over Lake Taupo in the centre of the island.
"A skydiving plane encountered an engine problem shortly after take-off. All parachutes including the pilot exited the plane and landed safely. There were 13 people on board," Skydive Taupo chief executive Roy Clements said in a statement.
A witness told the New Zealand Herald he heard a bang, then the skydivers bailed out and their parachutes opened despite the low altitude.
"It sounded like an engine blowing up. It would've been no longer than 15 seconds between the bang and when the skydivers started jumping out of the plane," he said.
Eves said the pilot was the last to jump moments before the aircraft nose-dived straight into the lake.
Civil Aviation Authority spokesman Mike Richards said it was miraculous no one was killed and an investigation was under way.
Taupo Mayor David Trewavas said the plane suffered a power failure at an altitude of about 4,000 feet (around 1,200 metres) and the pilot decided to evacuate the aircraft.
By comparison, tandem skydivers usually deploy their parachutes at around 5,000 feet.
"All the precautions were taken and they evacuated the plane safely. The plane then crashed into the lake at a place called Loafer's Paradise," he said.