Cairngorm Mountain Rescue Team said two climbers had been on the Aladdin's mirror ice route when one of them slipped. The other contacted police at about 14:20 on Tuesday.
A coastguard helicopter, which was training in the area, flew mountain rescuers and equipment to the scene.
The climber who suffered a leg fracture was carried to safety on a stretcher.
He was taken to Raigmore Hospital in Inverness.
Cairngorm MRT leader Willie Anderson told BBC Scotland: "The two climbers were still attached to the ice with ice screws and the uninjured one had made a ledge for them.
"It was really fortunate that the coastguard helicopter was training in the Cairngorms and was able to get the team members and equipment up the hill and as close to them as possible."
Falling snow and poor visibility meant the helicopter had to leave the scene and the casualty was stretchered out to a car park area rather than being airlifted.
Mr Anderson added: "Anyone who has a fall in the hills in the winter, the quicker you can get to them, the better. We were quite pleased with how the rescue operation went."
A climber has been rescued after falling on Coire an t-Sneachda in the Cairngorm mountain range.