Protest against fleet
The Nisshin Maru is the 8,000 tonne flagship of the Japan whaling fleet in the Southern Ocean.
It is one of at least two ships in the Japanese whaling fleet that has been targeted in recent days by anti-whaling activists from the Sea Shepherd group.
Protesters have thrown acid and other objects on the Japanese whaling vessels to try to stop them hunting whales.
Two Sea Shepherd ships collided with the Kaiko Maru whaler on Monday during a protest.
The Sea Shepherd vessels involved in that collision left the area on Wednesday after running low on fuel.
Neither boat was involved in the fire on the Nisshin Maru.
Senior crew closed hatches on the Nisshin Maru to seal off the burning area - apparently a processing plant inside the ship - to prevent it from spreading.
The fire was believed to be under control, Moronuki said.
Corbett said it was not clear if the missing crewman was inside the ship or went overboard into the icy waters of the Ross Sea.
"The ship has lost all engine power," he said. "The crew are still fighting [the fire], but with 20 people on board they are confident it won't sink and the fire won't spread further."
Chris Carter, New Zealand's conservation minister, said his government was drawing up contingency plans in the event of an oil spill.
"I wish the Japanese crew fighting the fire on the Nisshin Maru every good fortune. Their efforts will be crucial to averting further catastrophe," he said in a statement.