The gondola plummeted about 7m (23ft) after a tree is believed to have fallen on to its support cable at around 10:20 (09:20 GMT) on Tuesday morning.
The rescue operation was described as extremely difficult because the slope beneath the gondola was very steep and hard for emergency workers to reach.
Austrian reports said the four involved were most likely Danish citizens.
Police said nothing appeared to be technically at fault with the cable car route, called the Acherkogelbahn, and there was no evidence of any human error.
“The gondola crashed in a very stony area, although the rescue chain functioned very well. The rescuers were on site immediately but the terrain made it very difficult and the helicopters couldn’t get there very easily,” Michaela Burger from the cable car company told Austrian public broadcaster ORF.
What is unclear is how a tree could have fallen on to the support cable. District police commandant Hubert Juen told the Kurier website that either a tree or branches landed directly on the mount to which the gondola was attached.
Dozens of other gondolas were attached to the support cable at the time of the accident but none were affected by the crash.
