Nidwalden canton police said the woman was alone in the Titlis Xpress ski gondola when it detached from the cable. The gondola had just left the Trübsee station and was climbing the middle section of the mountain when the accident appears to have happened.
Police said air rescue service, ambulances and police officers were involved in the rescue operation.
Another video published on social media showed a group of rescuers moving to the crash site in deep snow.
One skier said “extremely strong winds” had left the gondolas swaying, and police spoke of gusts of more than 80km/h (50mph). The gondola service is normally suspended when winds climb above 60km/h.
“My mother looked at me and said suddenly – look, a gondola is falling. She pretty much heard the impact of the gondola and saw how it fell,” the skier told the Nau.ch website.
Beren Akkaya, one of several schoolchildren at a local ski camp, also witnessed the crash.
“I was really shocked. We were then afraid to go back down in the gondola,” the 14-year-old told the Blick website.
The cable car service was suspended, and public broadcaster SRF said between 100 and 200 passengers were brought to safety from about 40 gondolas.
The managers of the ski lifts expressed their shock at the accident and director Norbert Patt said “our thoughts are with the victim’s loved ones”.