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Police confirmed the incident happened about 1.30pm on Thursday and involved three trampers on the South Island mountain.
One person died in the incident, a second has minor injuries and the third was not hurt.
The person who sustained minor injuries was transported to Twizel in Canterbury for medical treatment.
Police remained at the scene late on Thursday night.
A New Zealand Mountain Safety Council (MSC) spokesman told The New Zealand Herald it was too soon to know how the avalanche was triggered, but there had been a moderate forecast risk.
"There was a moderate forecast at the time for that region, which is the second-lowest rating and just above low," the spokesman said.
"What that means is natural avalanches are unlikely. Human triggered avalanches are possible, usually small avalanches in specific areas or large avalanches in isolated areas.
"Just because it's a moderate danger doesn't mean there's no danger - that's one of the things to really get across to people."
MetService said Aoraki/Mount Cook's weather for Thursday was fine spells, with a chance of a shower or two with light winds and a high of 18degC.
The MSC spokesman said there was a risk of loose, wet avalanches at the time above 12,000 metres.
"There's various types of snowpack conditions, so loose and wet is as it sounds," he said.
"It's quite a slushy, icy mixture. That condition can mean that sort of avalanche can run a lot further than a typical slab avalanche which is nicely bound together."
The latest tragedy comes after two mountain guides were killed in an avalanche on Mt Hicks last month that also buried adventurer and philanthropist Jo Morgan.
Morgan managed to dig herself out and said at the time she was "gobsmacked" to be alive.
Her climbing partners Martin Hess and Wolfgang Maier - who are both originally from Germany but had become New Zealand residents - could not be resuscitated by rescuers.
Mr Hess was based in Central Otago and joined the New Zealand Mountain Guides Association in 2006.
Morgan had been roped to the two experienced mountain guides when the avalanche hit, but she was unable to find them after being sent tumbling up to 200m down the mountain.
“None of us had any control over it.”
Morgan was rescued after setting of a personal locator beacon.