The 121-pound dog "collapsed" while descending from the mountain with her owners.
"Displaying signs of pain in her rear legs and refusing to move, Daisy’s owners were able to keep her well hydrated and fed until team members were able to get on scene with a stretcher to help get them moving again quickly as the weather was due to deteriorate later that evening," the group said.
While canines make up about a dozen of the rescued each year for the group, the incident on Friday was the first involving a St. Bernard.
The operation lasted some five hours, as 16 members of the rescue team carried Daisy on a stretcher over obstacles, including a waterfall.
Video shows the rescue crew, all wearing masks due to the coronavirus pandemic, bringing the dog downhill.
Officials said that after seeking advice about pain relief, they were able to get a "little persuasion" out of Daisy with "plenty" of treats, and managed to administer some analgesia for the trip down.
"Daisy very quickly settled down with her chin resting on the head guard, having realized that we were trying to help her," the group said, adding she was "extremely placid and compliant."
Daisy, who "had a hard start in life" until she was rescued by her current owners a few months ago, is reported to be in good condition after the mountain rescue and in "her usual high spirits."
"She apparently feels a bit guilty and slightly embarrassed about letting down the image of her cousins bouncing across the Alpine snows with barrels of brandy around their necks," the rescue group said.
The St Bernard is a breed of large working dogs that were originally bred to rescue people in the Italian and Swiss Alps. They are usually on the other side of such mountain rescues.
"A massive whole 55kg thank you to Daisy St. Bernard who was so well behaved throughout the whole rescue, the perfect casualty you could say," the rescue group said.