Poonam Bhattal was with her schoolmates from Guru Nanak Sikh Academy in Hayes, west London, when she fell 20-feet from a chairlift at the resort of Claviere on Friday morning.
Emergency services attended to her but she died in an ambulance while being taken to hospital in Susa, about 40 kilometres from Claviere.
Italian police are investigating the accident and Skibound, which organised the trip, has also launched a probe into the safety of the ski-lift at the resort.
"Now there is an investigation in progress to understand how she can fall down with the safety bar closed. Before she fell down she was grabbing for the safety bar and the men [operating] the lift saw this, stopped the lift... But it was too late," said Marco Steffanini, director of the ski school at the resort.
In a statement, Bhattal's school confirmed her family had been contacted by the school's principal, Rajinder Singh Sandhu, to break the news of the teenager's death and her parents are believed to be on their way to Italy.
"It transpired that the parents were away from home for a few days. The principal contacted the family by telephone to ensure that they heard the tragic news from him personally.
The leader of this trip and everyone associated with it is devastated by the death of an absolutely lovely student. Our thoughts are with the family and all others in the community affected by this tragedy," the statement said.
"The vice-principal leading the trip has vast experience, having led 28 of such trips throughout his teaching career. He is obsessive about safety and security on these trips. It would be inappropriate for the school to comment further, given that there must be no prejudice to the very thorough investigation that will take place by Italian authorities," it added.
Meanwhile, tributes were also pouring in for the "beautiful girl" from Langley in Slough on social networking sites.
"She was a really bubbly person. She was really happy and never down. She was kind to everyone and she was very popular," said schoolmate and close friend Amanpreet Kang.
The group of students were led by 11 members of staff on a seven-day ski trip to Claviere, a ski resort in the province of Turin, which crosses the French border.
"We can confirm the death of a British National on Friday 22 February in Italy. We are providing consular assistance at this sad time," a British Foreign & Commonwealth Office spokesperson said.
London: A 13-year-old Indian-origin girl from Britain has died in an accident on a school ski trip in the Italian Alps.
First Published: Saturday, February 23, 2013, 21:11