Pavlina Pizova said she and Ondrej Petr began hiking the Routeburn track in Fiordland National Park on 26 July, but got lost in bad conditions.
After one night in the open, Petr, 27, slipped in a steep ice slope and died, Ms Pizova told reporters.
She said she spent the night with his body before moving on to find shelter.
She then stayed in a hut for almost a month.
Ms Pizova was found by a search team near Lake Mackenzie on Wednesday. Rescuers said she was "ecstatic" to be found and was in reasonable health.
Rescuers were alerted after Czech Consul Vladka Kennett spotted "a random Facebook post" by concerned relatives of Ms Pizova at home in the Czech Republic.
Ms Pizova was taken to hospital where she was interviewed by police, who described the case as "very unusual".
She told police that she and Petr, who was also Czech, set out to hike the Routeburn track between Mount Aspiring and Fiordland National Parks.
"The conditions were extreme. We encountered heavy snowfall and low cloud which contributed to our enforced overnighting in the open," Ms Pizova told a press conference.
"In our attempt to reach the hut, the tragic accident happened."
Ms Kennett said the hiker was unable to save her partner.
"Pavlina slipped behind him, and was unable to help him out, and that was it," Ms Kennett said. "She stayed with him for the first night, beside him, because first of all she wanted to be with him, and she couldn't move any further due to the weather conditions."
Petr's body has now been recovered by police and a coroner's inquiry launched.
Ms Pizova then spent another night out in the open, Ms Kennett said, stuffing all of her things into her sleeping bag and rubbing her feet continuously to avoid frostbite and hypothermia.
She later reached Lake Mackenzie Hut, 2km away, and broke in to the warden's quarters through a window. There she found food, firewood and supplies. She would stay in the small hut for nearly a month.
Ms Pizova attempted twice to walk out from the hut but was discouraged by the poor state of her feet and the deep snow. She used fire ash to make a letter ``H'' in the snow to signal for help.
"As you can imagine the last month was very harrowing for me," she said.
"She is an extremely tough woman," Ms Kennett added.
No search was launched initially as the couple had neither registered their hike with authorities nor were carrying emergency locator beacons.
After being alerted to the Facebook post, police found the couple's car, apparently parked for some time at one end of their route, and used a search helicopter to help locate Ms Pizova.
The Routeburn track usually takes a few days to complete.
Local police Insp Olaf Jensen said it was "very unusual for someone to be missing in the New Zealand bush for such a long period without it being reported", the New Zealand Herald reported.
"I appreciate there are a number of unanswered questions, however, until we can piece together exactly what has happened we are unable to say anything further."
A Czech hiker who went missing a month ago in the snowy mountains of New Zealand has described the "harrowing" ordeal in which her partner died.