The city of Auckland is so short of housing that the government will now pay up to 5,000 New Zealand dollars for people to up sticks and find another town.

The relocation grant is available to social housing tenants from Monday and a government announcement said more than 130 people had already expressed an interest.

"For those people who may want to move to cheaper regions where they may have family and other support networks, this grant will remove the cost barrier that may be preventing them from making the move," New Zealand's Social Housing Minister Paula Bennett said in statement on the government's website.

The scheme, announced in January, was originally targeted at people on the social housing register but has been extended to homeless people as media reports exposed a growing number of families living in cars, tents and garages.

In May, a Salvation Army spokesman said some streets in South Auckland had people living in every garage.

In 2014, HSBC described New Zealand as a "rock star economy" but high levels of immigration and a number of people relocating to Auckland in particular, have put pressure on housing affordability.

Prices in the country were up 12.4 percent in May on annual terms, according to an index by Quotable Value, a government-owned property research company.

And at its April policy meeting, the Reserve Bank of New Zealand Governor Graeme Wheeler voiced some concern about property prices, particularly in Auckland.

"There are some indications that house price inflation in Auckland may be picking up. House prices remain at very high levels and additional housing supply is needed," the statement read.