Rescue Co-ordination Centre search and rescue mission co-ordinator Dave Wilson said the man, in his 60s, required "some serious medical attention".
He was flown off the mountain by helicopter to Queenstown Hospital and then to Dunedin Hospital.
The centre was alerted at about 11am by a personal locator beacon carried by the party of four climbers, and a Helicopter Line helicopter flew the rescue team to the scene of the fall, near the Gillespie Pass at an altitude of about 1300m.
Const. Andrew said the rescue was made easier by the actions of others in the party.
Aware a helicopter would be on the way, one member of the party remained at a higher altitude with bright clothing.
He was spotted from the helicopter and the rescue went reasonably smoothly after that.
The four male climbers are understood to have all been New Zealanders ranging in age from about 20.
Mr Wilson said the incident showed the value of carrying a distress beacon registered on the website www.beacons.org.nz "Because it was registered, we were quickly able to establish from the party's emergency contact the make-up of the party and their climbing intentions.
"It has enabled the injured person to get medical attention as quickly as possible."
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