According to preliminary information from rescue services, up to 15 people could be in the area of the incident. The search for possible victims is carried out with the help of teams of dog handlers and five helicopters.
According to the Corriere della Sera newspaper, at least seven people were injured in the collapse, who were taken to hospitals in the neighboring cities of Bolzano, Trento, Belluno and Treviso.
The glacier collapsed near the tourist route to the summit of Punta Rocca, the newspaper added.
According to local media, record temperatures of 10 degrees Celsius (50 degrees Fahrenheit) were recorded in the area the day before the collapse.
The Marmolada glacier is the largest glacier in the Dolomites, which is part of the Italian Alps.