The spokesman, who declined to give his name, said he and another paramedic trekked about 40 minutes to the base of the glacier, where the woman lay unconscious in a tent with two broken legs and a head injury.
"What they think's happened is she was abseiling a pitch on the side of the glacier and her snow anchor came out and she fell about 300 metres," he said.
"It was ice and hard-packed snow and it was steep, probably around 50 degrees."
She had been wearing a helmet but it had come off in the fall.
The paramedics stabilised her broken limbs as best they could and packed her into a survival bag in preparation for the trip back across the ice.
As they did they heard the thundering noise of an avalanche close by.
"It did sound very close and very loud. You could feel the vibrations through the ground."
They could not see the avalanche but the helicopter pilot, who was waiting at the other end of the glacier, had a good view and said it looked "massive".
"He said it looked very large and very close to our little lights."
With the help of the two other climbers - who the spokesman said did an "awesome" job - they slid the woman across the ice to the waiting helicopter and flew her to Christchurch Hospital.
Canterbury District Health Board media advisor Amy Milne said the woman remained in a critical condition this morning.
The two other climbers remained at the glacier overnight and were organising for a private helicopter to transport them out of the area today.
Rescue Coordination Centre New Zealand search and rescue officer Chris Henshaw said the incident was a stark illustration of how carrying a personal locator beacon (PLB) saves lives.
"Had the party not been able to quickly make contact with search and rescue authorities, there is no doubt that the woman could have died, given the environment and the extent of her injuries," he said.
"This rescue provides yet another example of the importance of people carrying a PLB when they set out on foot or by boat. Registering the beacon means the owner's emergency contacts can provide details of the planned trip and rescuers can get to them faster."
The incident follows three deaths on the country's mountains in the last 10 days.
Yesterday, Swedish extreme-altitude skier Magnus Kastengren plunged 600m to his death near the peak of the country's highest mountain, Aoraki / Mt Cook, after slipping off a ridge.
Only four days earlier the 31-year-old had set a new record by completing a continuous descent of the mountain's east face.
On Labour weekend, Nicole Sutton and Hiroki Ogawa died on Mt Taranaki in the central North Island after the weather turned blizzard.
New Zealand Alpine Club general manager Sam Newton said although the three incidents were not linked, all had occurred at a very popular time for mountaineering.
"October, November, December is a popular time for classic mountaineering in New Zealand because there is generally good snow cover and the days are getting longer."
