
The man, believed to be a tourist, fell from the north-west ridge, the most commonly-climbed path to the mountain's 3,000-metre peak, and onto a glacier, police said.
The climber was a Czech man in his mid-20s, the New Zealand Herald reported.
Police however had not yet confirmed the man's identity.
It took the volunteer Wanaka Police Search and Rescue three hours to locate and recover the man's body.
The climber's death was a tragedy, rescue coordinator Sergeant Aaron Nicholson said.
"The very busy start to the summer outdoor season is a sobering reminder of the inherent risks in mountaineering," Nicholson said.