An Australian tourist died on Saturday afternoon while on a guided trip to Franz Josef Glacier.
He was on a day-long hike with a party of about 12 people being led by Franz Josef Glacier Guides, a company owned by Ngai Tahu Tourism.
Police say the group was negotiating a crevasse when the 38-year-old slipped and fell up to six metres, before losing consciousness.
He was flown to Franz Josef township but paramedics there could not revive him.
Ngai Tahu Tourism's chief executive, John Thorburn, says his staff are shocked and upset, and a full investigation into the incident has begun.
Police say Interpol is trying to contact the dead man's next of kin, who do not live in Australia.