Italian authorities closed roads and evacuated mountain cabins after experts warned that part of the glacier on Mont Blanc could collapse.
About 250,000 cubic meters of ice are in danger of separating from the Planpincieux glacier at the Grandes Jorasses peak, authorities said.
The mayor of the nearby city of Courmayeur said global warming was changing the mountain.
The Mont Blanc massif is the highest mountain range in Western Europe.
It has 11 peaks above 4,000m in France and Italy and attracts hundreds of thousands of tourists each year.
On Tuesday, the mayor of Courmayeur, Stefano Miserocchi, signed a road closure order in Val Ferret on the Italian side of Mont Blanc, after experts warned that a section of the glacier was sliding at speeds of 50-60 cm ( 16-23 inches) per day.
He said there was no threat to residential areas or tourist facilities, but mountain cabins in the Rochefort area were being evacuated as a precaution.
"These phenomena show once again how the mountain is going through a period of great changes due to climatic factors and is therefore particularly vulnerable," Miserocchi told Italian media.
Experts from the regional government of Valle d'Aosta and the Fondazione Montagna Sicura (Safe Mountain Foundation) say it is impossible to predict exactly when the ice mass might collapse.
The Planpincieux glacier has been closely monitored since 2013 in an attempt to establish how often the ice melts. But authorities warn that there is no "alert system."
In a weather-related incident in August 2018, an elderly couple was killed near Planpincieux in Courmayeur when their car was swept off a road into a valley during a landslide. Hundreds of people were evacuated, some of them by helicopter.
Rising global temperatures are causing the melting of mountain glaciers and the retreat of polar ice caps.
Earlier this month, dozens of people participated in a "funeral march" to commemorate the disappearance of the Pizol glacier in northeastern Switzerland.
The glacier, in the Glarus Alps, has shrunk to a small fraction of its original size.
Scientists say it has lost at least 80% of its volume since 2006, a trend accelerated by rising global temperatures.
Last month, a ceremony was held in Iceland to commemorate a glacier that was officially declared dead five years ago.
Earlier this year, tourists on the island captured a section of another glacier, Breiðamerkurjökull, which broke away, causing a large wave.