The 30-year-old adventurer had been in a coma since she was ripped down by an avalanche and had to be dug out from the snow while shooting a movie in Farrellones in Chile last Thursday.
On Monday the Swedish Ski Assocation confirmed that she had passed away in intensive care, due to complications caused by the lack of oxygen while buried in the snow.
“It is a terrible event with a sad outcome which is very hard to take in. Our thoughts are with Matilda's loved ones and we will do everything we can to support them at this difficult time,” said Tommy Eliasson Winter, the association's head of alpine sports.
Her manager Håkan Hansson told broadcaster SVT last week that the accident happened when Rapaport was skiing down the slopes on her own.
“She is one of the world's best skiers, but there was too much snow and she fell in the snow. She was wearing all the safety equipment, but did not have time to release the airbag because she was so focused on outrunning the avalanche,” he said at the time.
Born in Stockholm, Rapaport moved to Switzerland in 2009, where she worked to promote Swiss tourism while competing on the Freeride World Qualified Tour. She was also involved in a series of film projects.
The freeskier leaves behind her husband, Swedish slalom star Mattias Hargin, who flew to Chile together with her mother after the accident.