Woods and Mahuta said the $28m would be used by the Hastings District Council.
It would enable the delivery of social and affordable housing alongside greenfield development opportunities.
It would generate and maintain jobs, provide construction activity and promote economic confidence in the Hastings District, they said.
Infrastructure support will be provided for the Te Taiwhenua o Heretaunga Waingākau housing development (Waingākau Housing Development Ltd) in Flaxmere.
Waingākau Village is set on 15.5 hectares of semi-rural land located in Kingsley Chatham, on the western edge of Flaxmere, with views towards Te Mata Peak and the Kaweka and Ruahine Ranges.
Its first stage will deliver about 50 homes, including Te Puni Kōkiri- funded Te Ara Mauwhare pathways to homeownership homes.
Work has already begun - the first residents moved in in January.
"I am delighted that the houses will be a mix of public housing, papakāinga and affordable housing on Māori land," Mahuta said.
"This reinforces my commitment to provide our whānau with warm, dry and safe housing across the motu."
The infrastructure funding will complement work already under way in Hastings to address housing need, particularly for low-moderate income households.
The Government funding has been committed through the $3 billion shovel-ready fund to help recovery from the coronavirus crisis.
The Ministry of Housing and Urban Development began work with the Hastings District Council, Kāinga Ora, Te Puni Kōkiri, Ngāti Kahungunu, the Ministry of Social Development and other key local players in April 2019, to respond collectively to housing need in Hastings.
As a result of the collaborative work, in December 2019 ministers announced a support package, which would provide around 200 additional houses for low-moderate income households by mid-2021.
Woods and Mahuta said this had been extended to the end of 2021 due to Covid-related delays.
The houses will be a mix of public housing, papakāinga affordable housing on Māori land, and other affordable housing. This includes an additional 160 public houses through Kāinga Ora – Homes and Communities (as well as replacing about 70 existing homes).