The expedition was hit while descending a peak in the Ishkoman Valley, located in the northern district of Ghizar.
Karrar Haidri, head of Pakistan's Alpine Club, told The Associated Press that the six surviving climbers were taken to a hospital in the nearby town of Gilgit for the treatment of injuries.
"Sadly, one Pakistani mountaineer was killed, but six other members of the expedition are being treated at a hospital," he said.
"A Pakistan army helicopter was used for this complicated but successful rescue operation, despite the fact that the stranded mountaineers were present at an altitude of around 5,300 meters," he added.
Ashraf Aman, a Pakistani tour operator who arranged the expedition, confirmed that Pakistan's military had dispatched the helicopter earlier on Tuesday morning to rescue the climbers.
He said the body of the Pakistani mountaineer, Mohammad Imtiaz, would be brought down later.
Aman said none of the surviving team had life threatening injuries.
The four Italian climbers involved are expedition leader Tarcisio Bellò, Luca Morellato, David Bergamin and Tino Toldo.
Bellò said they were "very lucky" that they survived. "I think glacier collapsed and millions tons come down. We were very up at the mountain," he said.
In a separate incident on Monday, two Chinese mountaineers were reported missing in another area in northern Pakistan, said Haidri. He said a rescue mission was planned to find them.
Mountaineers from across the world travel to Pakistan every year to try scaling its high northern mountains. Harsh weather and conditions often prove a test for the most experienced of climbers.
Earlier this year, two European climbers —Italian Daniele Nardi and Briton Tom Ballard — were killed during bad winter weather on Nanga Parbat, which is the world's ninth-tallest mountain at 8,126 meters (26,660 feet).
Nardi, from near Rome, had attempted to scale the peak in winter several times. Ballard's disappearance hit his homeland particularly hard as he is the son of Alison Hargreaves, the first woman to scale Mount Everest alone.
She died at age 33 descending the summit of K2.