That followed the deaths of three dolphins on the South Island's east coast earlier in the summer, and another case where one dolphin was accidentally caught and killed.
FNZ inshore fisheries manager Steve Halley said the number of captures in such a short time was unusual and warranted investigation.
"Hector's dolphins are nationally endangered taonga and any capture is very disappointing," he said.
"We're working alongside DOC to update a plan to manage the threats to Hector's dolphins from a range of causes, including fishing."
The Hector's dolphin Threat Management Plan involved a programme that included research, information gathering and initiatives to mitigate and avoid interactions between fishing and dolphins.
These latest captures would be factored into the review of the plan, alongside with other scientific analysis, Halley said.
"In the meantime, we are talking with fishing companies which operate in the area to better understand how this happened," he said.
"Timely information is key to our ability to protect these dolphins, so it was good that the vessel reported the captures immediately."
FINZ chief executive Dr Jeremy Helson described the spate as a "regrettable and unprecedented run of deaths" and said the industry was "extremely concerned".
"We are throwing all our resources into finding out why this is occurring with unusual regularity and we are heading down to Canterbury to talk to the fishers involved."
Forest and Bird responded to the deaths by calling for an end to trawling in the habitat.
"It is just so disheartening to receive endless news of endangered species dying in nets and on lines at sea," spokesman Anton van Helden said.
"What is abundantly obvious is that trawling in endangered dolphin territory is a recipe for disaster, and it must end.
"One small reserve for dolphins near Banks Peninsula is hopelessly inadequate, when we know these animals live around the coast of the South Island, and swim as far out as 20 nautical miles."
Van Helden commended the fishers for doing the right thing and reporting the deaths – but argued the need for electronic monitoring on fishing vessels.
"These dolphins were correctly reported, but the fact is, [the Ministry for Primary Industries] have no idea what is being pulled up in the nets of hundreds of boats all around our coastline," he said.
"Without observers or cameras on most boats, we have no idea how many dolphins are killed every year, and no ability to protect them."
