The vessel in distress off the east coast of D'Urville Island in the Marlborough Sounds is now being towed to safety in French Pass.
Rescue Coordination Centre spokesperson Steve Rendle said the vessel, which is believed to have five people on board, issued a mayday call about 1.30pm.
The vessel had been making its way to French Pass, for treatment for a passenger understood to have a broken leg, when it began taking on water and the emergency call was made.
Nelson-based charter company Seabird Charters is towing the vessel back to safety from the Rangitoto island group near D'Urville Island, where it had anchored.
Seabird Charters co-owner Barry Bird said the Nelson-based vessel had been at risk of sinking but was now safe.
"As I understand it, the guy had been on the boat and slipped and broke his ankle, and then the boat has taken on a lot of water," Mr Bird said.
"They had a pretty good risk of sinking but they soon got that under control."
He said the crew was busy bailing water from the boat while it was being towed to French Pass.
"We've got some pumps on there and the boys are pumping flat-out as we speak," Mr Bird said.
It was unclear at this point whether it would be able to be towed back to Nelson.
Mr Rendle said it was also unclear what caused the boat to take on water.
The Nelson Marlborough Rescue Helicopter has flown the injured passenger to Nelson Hospital.