The three climbers died at an altitude of around 3,600 meters at around 10.30 am, according to mountain rescue teams.
The tragedy took place on the Dômes de Miage mountain peaks in the southern area of the Mont Blanc massif.
The climbers, who were from the same roped party, appear to have fallen as a result of their climbing bolts coming unscrewed, according to the rescue teams.
The identity of the victims remains unknown and the rescue operation is still ongoing.
The tragedy comes just a few days after four climbers — including an Italian man and two French women — died in the French Alps on Sunday in three separate accidents, the local prosecutor's office said.
Mont-Blanc has been under restricted access since mid-July due to the fact that there have been too many people trying to climb in the massif at this time of year following an order by the Haute-Savoie prefecture.