The aim is to boost the overall population and broaden the gene pool of the endangered species but some members of the island's supporters group are distressed by the move.
The department is looking for a new site to house the growing population and establish a self-sustaining population. The Herald on Sunday understands a site in the Kahurangi National Park in the northwest of the South Island is favoured.
The moves could leave Tiritiri Matangi with as few as four takahe.
Some members of the Supporters of Tiritiri Matangi are worried about the impact on the island's advocacy and educational role.
The group's chairman, Brian Chandler, said while the transfer programme was expected to boost overall numbers, the value of the public being able to see takahe was also important.
"The wellbeing of the species is also dependent on the public perception of the species. It's really important that we get the public onside."
About 35,000 people, including 7000 school children visit the island a year.
"Unfortunately the takahe likely to be moved are the ones the visitors see most often," Chandler said.
That included a family of four that had made their home near the lighthouse and visitor centre and were used to people.
"I guide on the island and the first thing visitors say is, 'I want to see a takahe'. There was a very good chance they would because of where those birds were living. We just can't guarantee that in the future."
DoC's takahe ranger, Phil Marsh, said the birds being moved this month were two single adult females which would make new high-value genetic pairings, and one juvenile which would be fostered to a takahe pair at Burwood.
"There, the birds will learn key behaviours such as tussock feeding in their native grassland habitat."
Tiritiri Matangi Island is one of 13 sites across New Zealand that provide crucial sanctuary for takahe breeding pairs, he said, but only Burwood has the natural tussock grassland of the takahe.
Size may also be a consideration for Tiritiri Matangi as a breeding pair can defend a territory of 5-60ha.
"The focus of the Takahe Recovery Programme continues to be a push towards returning takahe to large areas of their former South Island range," Marsh said. "While secure sites such as Tiritiri Matangi offer habitat in the short-to-medium term, they don't have the ability to hold self-sustaining populations.
"The juvenile from Tiritiri Matangi will be one of 12 nationwide that is fostered at Burwood this year to learn the vital skill of tussock feeding. Learning how to forage on tussock is key to establishing future wild populations."
Takahe file
•There are about 300 in the world - all in New Zealand.
•The flightless birds were thought to be extinct until being rediscovered in 1948 in the Murchison Mountains of Fiordland.
•13 sites have breeding pairs, including a population recovery site near Te Anau.
• Places to see the birds include Tiritiri Matangi, Motutapu Island, Tawharanui Regional Park, Auckland Zoo; Maungatautari sanctuary, Waikato; Zealandia Sanctuary, Wellington.
•Numbers on Tiritiri Matangi are being reduced from nine to possibly four.