"The boat crew reported that on Monday night, six crew members abandoned the vessel.
"One person was aboard a life-raft ... the other five entering the water without lifejackets."
The circumstances of the incident have not been confirmed by authorities.
However, Fijian media outlets are reporting that an alleged "horrific" incident on board had prompted some of the crew to jump overboard.
The RNZAF crew carried out a search in the area and found an upturned life-raft with one person on it, the spokesman said.
A local patrol boat was able to drop a survival pack including food, a radio and a beacon to the person on the life-raft.
"The Orion remained in the vicinity of the life-raft as long as its fuel situation would allow, to assist [the patrol boat] before returning to Whenuapai."
The survivor was eventually taken to shore. The remaining five crew members remain missing.
Commander Timoci Natuva, head of the Fijian Navy, told the Fiji Sun their focus now was on saving lives.
"Once we interview the survivor, we can get a better understanding of what actually happened - which the police will deal with, as the evidence dictates."
The fishing vessel is said to be a Fiji-flagged offshore longliner that has Fijian and foreign crew members.