The woman, from the Czech Republic, was found on Wednesday, living in a park warden's hut on the snowed-in Routeburn Track, Inspector Olaf Jensen told reporters.

She was admitted to a local hospital and found to be in reasonable health, he said, although she remained upset after her ordeal.

He said the young couple set off on July 26 to hike the 32km track, a route which typically takes three days. But Mr Jensen said the couple became lost because the track markers were buried in deep snow.

He said that, two days into their ordeal, the man fell down a steep slope and died.

The woman then spent the next three nights living outside in freezing conditions before stumbling upon the hut and breaking in. He said she suffered from some frostbite, hypothermia and other minor injuries.

"Given her experience and the avalanche risk, she decided it was best for her safety to remain in the hut, and that was the correct decision to make," Mr Jensen said.

He said the woman fashioned a letter "H'' in the snow outside to signal that she needed help, and waited. But Mr Jensen said hikers were avoiding the route and nobody came.

"It was not passable," he said. "It was really extreme conditions."

Mr Jensen said it was almost a month before the Czech consulate finally raised the alarm on Wednesday. He said police found the couple's car at the trailhead and sent a helicopter along the route. He said the woman was relieved to see her rescuers after her traumatic experience.

"It's very unusual for someone to be missing in the New Zealand bush for such a long period without it being reported," Mr Jensen said.

He said there was a radio in the hut but the woman could not get it to work.

Geoff Owen, the Wakatipu-area operations manager for the Department of Conservation, said the Lake Mackenzie Hut where the woman stayed had firewood and may have had some food left behind by the rangers. He said the woman may have also broken into another hut nearby to find more food.

The Routeburn Track, on South Island, is listed among New Zealand's top 10 Great Walks and is popular with tourists during the Southern Hemisphere summer.

But during the winter months from June until August it can become treacherous. When there is deep snow, it is typically only tackled by climbers equipped with crampons and ice axes.

Mr Jensen said the couple were reasonably well equipped for a hike but not for the conditions they encountered.

Richard Forbes, the president of the Otago Tramping and Mountaineering Club, said he was with a group of hikers that went to the Routeburn Track last weekend.

He said they were advised by Department of Conservation staff not to hike the alpine section of the track, where the woman was later found, because of the avalanche risk.

Police said they plan to try to recover the body of the man, who was also from the Czech Republic.