About 250,000 cubic metres of ice are in danger of breaking away from the Planpincieux glacier on the Grandes Jorasses peak, officials said.
The mayor of the nearby town of Courmayeur said global warming was changing the mountain.
The Mont Blanc massif is Western Europe's highest mountain range.
It has 11 peaks above 4,000m in France and Italy and attracts hundreds of thousands of tourists every year.
On Tuesday, Courmayeur Mayor Stefano Miserocchi signed an order closing roads in the Val Ferret on the Italian side of Mont Blanc, after experts warned that a section of the glacier was sliding at speeds of 50-60cm (16-23in) per day.
He said there was no threat to residential areas or tourist facilities but mountain huts in the Rochefort area were being evacuated as a precaution.
"These phenomena once again show how the mountain is going through a period of major change due to climate factors and, therefore, it is particularly vulnerable," Mr Miserocchi told Italian media.
Experts from the Valle d'Aosta regional government and the Fondazione Montagna Sicura (Safe Mountain Foundation) say it is impossible to predict exactly when the mass of ice would collapse.
Rising global temperatures are causing the melting of mountain glaciers and the retreat of polar ice sheets.
Earlier this month, dozens of people took part in a "funeral march" to mark the disappearance of the Pizol glacier in north-east Switzerland.
The glacier, in the Glarus Alps, has shrunk to a tiny fraction of its original size.
Scientists say it has lost at least 80% of its volume just since 2006, a trend accelerated by rising global temperatures.
More about: Mont-Blanc climate
