It was not clear how the man came to be injured.
New Zealand salvage manager Bruce Anderson confirmed a crew member fell onto the rating while transferring off the cargo ship onto a navy boat.
Meanwhile, the union representing New Zealand maritime workers says the crew on the stranded cargo ship would have been fearing for their lives when the vessel tipped by about 4 degrees overnight,
The 17, mostly Filipino, crew members issued a mayday call when the ship crushed the reef it was resting on and shifted back a few degrees from its 10-degree list.
One of the crew suffered minor injuries when they were bundled onto transport this morning and taken to Tauranga Airport, where they are off-limits to media.
Non-essential crew had been taken off the vessel as a precaution earlier.
A Maritime New Zealand spokeswoman said the crew issued the mayday call as a "standard precautionary measure''.
"They do the mayday call as that is the way to get them off quickly,'' she said.
Maritime Union general secretary Joe Fleetwood did not accept this and said the crew would have been fearing for their lives.
"It wouldn't have bee a precautionary thing. As soon as you hit that button you're in distress. They probably feared for their safety, thinking this vessel's going to snap in half or roll over and kill everyone on board.
"I guarantee they would have been terrified.''
Mr Fleetwood said that if it had been a New Zealand crew they would not have stayed on the vessel for the six days since the Rena struck Astrolabe Reef off Tauranga.
"If that was a New Zealand crew they would have been off the ship straight away. If that was an Australian crew they would have been off and done. They're Filipinos, and what I believe is they're treating them with contempt and telling them `just stay there and do your job'. I've called for Maritime New Zealand to release all their reports so we can know who made all these decisions.''
Maritime New Zealand said the crew would go back onto the ship once it was deemed safe to do so, but Mr Fleetwood doubted this would ever be the case.
"Every time it moves an inch it's putting so much stress and pressure on the vessel, slowly but surely ripping and ripping and ripping it and, mate, once you fracture the keel - that's the strongest part of the vessel - it breaks in half, or it breaks in three.
"The ship's run aground and it's not designed to run aground. I believe the crew and also the environment are at risk. It has the potential to be the biggest maritime disaster New Zealand's ever seen, other than the Wahine (ferry disaster in 1968).''
Mr Fleetwood said he had been calling on the New Zealand Government to buy an emergency oil spill response vessel "for years'' but to no avail.
"Now we're caught with our pants down and now we're looking to (salvage company) Svitzer to get their clean-up vessels from Singapore.''
A Maritime New Zealand spokeswoman said the crew members were "all doing OK''.
"They're all obviously just quite tired. They've been through an ordeal so as you can imaging they're probably quite stressed as well.''
