Payments could be at a similar level to the $3000 offered to people after the earthquakes to relocate to Christchurch and take up full-time work, she said.
The proposal has received mixed support. Provincial leaders are welcoming the idea, while others have questioned whether the regions have adequate social services for vulnerable tenants.
Mrs Bennett singled out Ashburton as a potential destination for South Aucklanders because of its strong Pacific Island community.
Ashburton's Mayor Angus McKay welcomed the suggestion, saying the council had been trying to entice newcomers into the region for years.
The South Island town had more jobs than workers, he said, so it would welcome any people who could fill that void.
Mangere Budgeting Services Trust chief executive Darryl Evans said the policy had some promise on paper, but the devil would be in the detail.
He said a key question was whether there were enough community agencies and support systems in place in the regions.
For those who needed mental health support, there were already limited resources, even in the cities, so the Government would need to ensure there was enough support in rural areas, Mr Evans said.
Housing New Zealand has been investigating which regions have the most state house vacancies.
Lower Hutt has been identified as the spot with the most available properties, followed by Porirua.
However, Hutt South Labour MP Trevor Mallard said shifting people to areas like Lower Hutt was not an option.
He said there were already hundreds on the waiting list, and more than a hundred state homes boarded up because they were earthquake-prone.
The strongest criticism of the policy came from Auckland Action Against Poverty spokeswoman Sue Bradford, who described it as "incoherent and racist". She said Mrs Bennett had failed to appreciate the connection between vacant houses and the absence of paid work.
She was also critical of the minister's suggestion that Pacific Islanders could be prime candidates for a move out of Auckland.
"While people on the Auckland state housing lists should have the option to move to another centre if they choose, this looks very much like a deliberate strategy to push poor, brown people out of the country's economic powerhouse," she said.