Services at nine other courts, including two shut for earthquake strengthening, will be scaled back significantly.
The Dargaville, Waihi, Te Awamutu, Te Kuiti, Opotiki, Marton, Waipukurau, Oamaru and Balclutha courts will be used only for specific hearings, rather than being open five days a week.
Other matters at the affected courts will be diverted to the nearest open courts.
Long-term decisions on the courts at Oamaru, Balclutha and Rangiora, which were closed last year due to earthquake risks, would be made next year.
Mr Borrows said the proposed changes - the first across the country's 63 district courts in 30 years - would come into effect early next year.
A spokesman for the minister said 31 jobs would go at the 13 courts facing closure or reduced hours, while a further 18 jobs would be created at regional hubs.
A Ministry of Justice spokesman said the proposed nationwide restructure would result in fewer than 200 positions being affected, most of them management roles.
There would be a net reduction of 68 staff, 66 of them in management roles - a figure which included the net losses at the courts facing closure or reduced hours.
Mr Borrows said the court at Whataroa was one of the least-used in the country, with only 11 sitting hours spread over four days last year - making it second only in lack of use to the court at the Chatham Islands.
Warkworth was also one of the least-used courts, sitting less than 20 full days last year.
The workloads at smaller courts had fallen consistently over recent years, a trend projected to continue as crime rates fell and changes from next July under the Criminal Procedures Act reduced the number of hearings.
The largest 10 courts dealt with 62 per cent of hearings, while the smallest 10 dealt with less than 1 per cent.
The changes from next July would involve the rollout of an electronic operating model, which would save more than 90,000 hours of police and court work.
Mr Borrows said court services could be accessed through many different channels including by post, telephone, internet, audio-visual links or a local Justice of the Peace.
There would be little change for communities, with the only time people needed to go to a courthouse being for appearances.
Law Society courthouse spokesman Iain Hutcheson said any decision to close or restrict hours at courts must ensure access to justice was maintained.
"There may be sound financial reasons for closing a courthouse, but the decision must ultimately be driven by ensuring the closure will improve the integrity of our justice system and retaining open access to the courts for all New Zealanders."
Public Service Association national secretary Richard Wagstaff said court staff were reeling over the scale of the job losses and the level of change being proposed.
He said staff would have to travel further to provide cover in areas where services were being cut back, and there would be extra work coming out of those courts which were closing.
Green Party courts spokesman David Clendon said shutting courts in small towns was about saving money and would reduce access to justice.
Victims would be forced to travel further to attend hearings and offenders would fail to appear, creating more work for police.
"The Government is basically saying if you are a smaller regional town you don't get the same access to justice as other communities," he said.
Labour's justice spokesman Charles Chauvel said the changes would impact on the ability of ordinary New Zealanders to access the justice system.
"Everyone understands the vital role that local courts play in their community. The closure of any inevitably means hundreds of people involved in either family or criminal proceedings will be disadvantaged."
The Ministry of Justice will consult with staff and stakeholders on how the changes, to be introduced by next March, would work.
