Justice Minister Andrew Little says a new law would need to be passed to deport Brenton Tarrant to Australia.
Earlier today Tarrant was sentenced to life without parole, the first time such a sentence has ever been passed in New Zealand.
In relation to the March 15 attacks last year, Tarrant admitted 51 charges of murder, 40 counts of attempted murder and one of engaging in a terrorist act laid under the Terrorism Suppression Act 2002.
The sentence has raised questions about whether Tarrant, an Australian national, could be deported.
But Prime Minister Jacinda Ardern said there was no legal basis to do so at the moment, and if there ever was, the wishes of the victims' families would be paramount.
Little told the Herald the only way an Australian could be deported was after the completion of their sentence.
"It's automatic if you're a non-citizen or non-resident. Any other way would have to be by agreement of treaty with the country of origin, and we don't have that with Australia.
"Our Corrections system is now obliged to detain him for life."
NZ First Leader Winston Peters called for Tarrant to be extradited.
"Now is the time for Australia's Minister of Home Affairs, Peter Dutton, to receive and carry out the terrorist's sentence in Australia," Peters said.
"The Islamic community and all of New Zealand has already suffered enough without having to pay astronomical prison costs to keep him safe in our prison system."
But Little said there was no statutory authority for New Zealand to simply ask Australia to take Tarrant.
"We would have to have a separate treaty or agreement. It's pretty clear people want him detained for life, so we'd need to get Australia's agreement to do that."
It would take years to get a treaty in place - which would be possible given Tarrant's life sentence - and would require new legislation, Little said.
"It's just not on the agenda at the moment."
Australian Prime Minister Scott Morrison released a statement about Tarrant's "cowardly and horrific crimes", but didn't mention deportation.
"It is right that we will never see or hear from him ever again," Morrison said.
"All Australians were horrified and devastated by his despicable act. New Zealand is family to us.
"Today, we send our love across 'the ditch' and I had the opportunity to pass on those wishes earlier today to New Zealand PM Jacinda Ardern."
Before the sentence came out, National leader Judith Collins was wary of deporting Tarrant, partly because Australians seemed keen to deport Kiwis who were midway through their sentence.
"That would mean New Zealand would either have a whole lot of criminals who have not served their sentences wandering around the communities, or else we'd have to find jail space for them," Collins said.
Little said Collins was being "populist".
He said Australia had three grounds to deport Kiwis back to New Zealand.
They were those who had completed a sentence that met a certain threshold, those who were a threat to the community, and the 501s, who have had visas to be in Australia cancelled on character grounds.