Although police in Peru said they did not have the identity of the man found, the missing climbers were named as Matteo Tagliabue, 27 and Enrico Broggi, 28, in the Italian newspaper La Repubblica.
The climber's body was found close to the the base of the 5,947-metre Alpamayo mountain and near the village of Caraz, while the search for his climbing partner is ongoing.
The pair went missing as they "headed to the summit, when a ledge broke off in the zone of the northeast face," rescue team chief Alfredo Quintanilla said on Tuesday.
He said the high-altitude search team included around ten rescue workers in two groups working in coordination with police.
Alpamayo features a daunting slope that renders an ascent particularly challenging, as well as pyramids of ice that have prompted the nickname among locals of "the most beautiful mountain in the world."
It is part of Peru's Cordillera Blanca, or "White Range", which stretches 180 kilometers (112 miles) and includes numerous peaks that soar 6,000 meters or higher.