The accident was in Sölden, 40km (25 miles) south-west of Innsbruck, said Edelbert Kohler, the head of criminal police in Innsbruck.
The helicopter was hauling goods to the top of the cable car lift for construction work when the 750kg (1,500lb) block of concrete fell, Mr Kohler said.
There have been conflicting reports over the number of people injured. Jakob Falkner, an executive of the cable car company, said four were hurt, and three in the cabins escaped injury. But Red Cross officials said seven were injured - five seriously.
Mr Falkner said some of the victims appeared to be foreigners, and children were among the injured.
Twelve rescue helicopters hovered over the accident, while emergency workers rushed to the scene on foot. More than 100 passengers were rescued from stranded cable cars.
The glacier skiing area around Sölden - some parts of which are as high as 3,000m (9,850ft) - is popular with summer tourists who flock to its perennially snow-covered alpine peaks.
The accident evoked memories of a ski lift tragedy in Italy, where a low-flying US Marine jet sliced a ski gondola's cables in 1998, killing 20 people.
Almost five years ago, 155 people were killed when a funicular ski train caught fire in a tunnel near Kaprun, 60 miles south of Salzburg, in Austria's worst peacetime disaster.Reuse content