"Private Mila was a popular member of the unit who was well known as a colourful character. He will be sorely missed by his comrades," a Defence Force Statement said.
Private Mila's brother is also a member of the New Zealand Army.
'Tragic accident'
Prime Minister John Key said he was shocked and saddened at Private Mila's death.
"This is a tragic accident and my heart goes out to the family of Private Mila. Our Defence Force in Afghanistan is operating in a dangerous and difficult environment in order to help the Afghan people.
"To have one of our own die in a road crash is heart-breaking news."
Mr Key later told media he stood by the decision to maintain a New Zealand presence in Afghanistan until the job there was done.
Staying put and continuing the work was a way of "honouring" Private Mila's death, he said.
Defence Minister Wayne Mapp said news of the crash was "tragic".
"The life of every New Zealand soldier is precious, not only to their own family but to the wider Defence family and the country they serve, he said.
"Private Mila was a fine member of the Defence Force who has served his country well, and has now paid the ultimate price while doing his duty.
"At this time we should all reflect on the price of his service."
Fatal patrol
Dr Mapp told media this morning the Humvee Private Mila had been travelling in was part of a four-vehicle humanitarian patrol.
The purpose of the patrol was to engage with the locals and show their presence in the area.
The chief of Defence Force, Lieutenant General Richard Rhys Jones, said Private Mila was the gunner who was on top of the vehicle.
"I spoke to his family this morning. They are upset. They are still coming to terms with the grief and the loss. It's always difficult when there is a death away from the family," Lieutenant General Jones said.
"You can imagine, it's a huge shock to the family," Dr Mapp said.
"It's so much more difficult when your loved one is thousands of miles away."
A sergeant was left with broken ribs after the crash and a private with serious head injuries including a fractured skull and damaged eye socket. Another private was shocked but without serious injury.
The sergeant was in a stable condition. The private with head injuries had been operated on, but remained in a serious condition.
They will be evacuated to Germany to the Nato hospital and later return to New Zealand.
Lieutenant General Jones said the crash was not connected with any insurgent activity and was an unfortunate road accident in a a steep and rocky area with treacherous roads.
"We emphasise driver training. There are difficult roads."
Lieutenant General Jones said it was not yet known if the road collapsed, or if there was driver error but that the Defence Force would conduct a thorough investigation.
The soldiers were well trained, but it was impossible to remove all the risks, he said.
"Everybody in the military understands the dangers they go through. But it's never easy to go through loss. Our sympathies go out to the families. It's never easy," Lieutenant General Jones said.
Gillard pays tribute
Australia's Prime Minister Julia Gillard paid tribute to Private Mila
when she gave an historic address in the House this morning
.
The New Zealand and Australian flags were flying at half-mast when she arrived at Parliament.
"The Anzac legend is not confined to records and books - it is a living story," she told Parliament. "The Anzac spirit lives on in the most strategically difficult theatre of our time - Afghanistan."
Ms Gillard said Australia grieved the loss of New Zealand soldiers as if they were their own.
"Australia has many alliances and friends around the world ... but New Zealand alone is family."
Sixth Afghanistan death for NZ
Private Kirifi Mila is the sixth New Zealand born soldier to have been killed in Afghanistan.
John 'Jack' Howard was serving with the British military when he was killed by a suspected incident of 'friendly fire' from a United States aircraft in December.
Feilding-raised soldier Lieutenant Tim O'Donnell, 28, was killed in a fierce firefight in Afghanistan last August.
He was the only soldier serving with the New Zealand military to be killed in overseas combat in 10 years.
In March last year, a New Zealand-born soldier in the Australian army, Corporal Mathew Hopkins, 21, of Christchurch, was shot dead in an intense fire-fight with Taleban insurgents near the village of Kakarak, 12km north of the Australian base at Tarin Kowt.
Former Aucklander Sean Patrick McCarthy, 25, a member of the Australian Special Air Service Regiment, was killed when his vehicle struck a roadside bomb in 2008.
Labour leader Phil Goff's nephew, US Army Captain Matthew Ferrara, was killed in Afghanistan in 2007.
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- NZHERALD STAFF