A rescue helicopter picked up the surviving climber shortly before midday and retrieved his partner's body about half an hour later.
Senior Constable Brent Swanson of Lake Tekapo police said the climber was not tethered to his partner at the time of the fall.
"He's basically fallen off the main ridge of Mt Cook, so it's very steep terrain.''
It was not yet known how the man had fallen, he said.
"We haven't even spoken to his partner properly yet. We'll be talking to his climbing partner later on this afternoon.''
Mr Swanson said the survivor had "a bit of scare'' but was uninjured.
Climbing conditions were good and the weather was fine at the time.
Both overseas climbers were very experienced, but Mr Swanson would not say which country they were from or how old they were.
"We're not indicating that until we've notified next of kin. It's obviously a very small community, the climbing fraternity.''
Police said the pair had gone into Aoraki Mt Cook National Park yesterday with the intention of climbing the 3754m-high mountain along the Porter Col route.
Last week, the climbers had successfully skied and climbed The Footstool and the east face of Aoraki Mt Cook.
Police said it was fortunate that members of the DoC alpine rescue team were training with land search and rescue staff in the park at the time of the accident.
A rescuer slung underneath a helicopter retrieved the man's body and his surviving partner using a strop line.
The climbing death is the second within a week after two climbers died on Mt Taranaki over Labour Weekend.
Nicole Sutton, 29, and her partner Hiroki Ogawa, 31, died after huddling in an ice cave for two nights when they became trapped near the summit in bad weather.
