Maritime New Zealand said 39 crew members from the Amaltal Columbia were transferred to the Russian fishing vessel, Ivan Golubets, which initially responded to the mayday call.
The other four crew, including the captain and the chief engineer, had also been transferred to the San Discovery which also came to the rescue.
The crew were now being taken back to Lyttelton. The 54-metre trawler is about 70km northeast of the Lyttelton Heads.
No injuries had been reported.
The Rescue Co-ordination Centre said it received an urgency call from the vessel at 5.24am alerting them to the fire. This was then upgraded to a mayday call about 5.40am.
The fire started in the meal hold in the stern of the vessel and has spread, Maritime New Zealand said.
There is a four metre swell in the area with winds of 30 knots.
A Royal New Zealand Air Force P3 Orion, which was in the area for a standard fisheries patrol, is monitoring the situation from above.
Search and rescue mission co-ordinator Conrad Reynecke said contingencies were being put in place to have helicopters from Christchurch, with winching capability, on standby.
Search and rescue mission co-ordinator Tracy Brickles said the safe transfer of crew off the vessel was an excellent result.
"The priority in these situations is always the safety of the crew. This is a good result in difficult conditions with winds of 30 knots and a swell of 4m. We would thank the masters of the Ivan Golubets and the San Discovery for their prompt response."
The Transport Accident Investigation Commission has launched an inquiry into the blaze. A spokesperson said two investigators have been assigned to the inquiry and are monitoring the situation from Wellington.
In 2005 the Amaltal Columbia grounded about 100 metres northwest of Town Wharf at Bluff, although it was refloated the same morning.
Maritime New Zealand spokesman Steve Rendle said Air Force personnel had observed the extent of the fire using thermal imaging equipment.
"[The fire] has spread reasonably ... there are heat spots showing around the starboard side," he said.
Mr Rendle said the blaze is "definitely not a fireball" as has been reported.
"It's largely smoke coming out of available openings. I don't think anyone has reported any flames [visible above deck], but that doesn't mean there isn't fire."
