The emergency services were alerted and Mr Shaw, from Argyll, was airlifted to Belford Hospital, where he later died of his injuries.
A spokesman for Police Scotland said: “Around 3.30pm on Sunday, the emergency services were alerted to a fallen climber near the East Gully, Aonach Mor, Ben Nevis.
“Following liaison with Lochaber Mountain Rescue Team and the coastguard, rescue helicopter 951 attended and uplifted the 21 year-old male climber to the Belford Hospital, where despite medical treatment he sadly succumbed to his injuries.
“The man’s identity can be confirmed as Kieran Shaw, aged 21, from Helensburgh, Argyll.”
Aonach Mor, which features Britain’s only mountain gondola, is a popular destination for climbers and tourists.