Beth Tweddle remains in hospital after neck surgery which involved having a piece of bone taken from her hip.
The 30-year-old, who won bronze at the London Games in 2012, fell on the slopes during rehearsals for celebrity sports show 'The Jump'.
Beth Tweddle
Tweddle described the last 48 hours as "very scary" after the operation which saw surgeons take a bone from her hip and use it along with pins to fuse together two fractured vertebrae in her neck.
The surgery has been hailed a success, and in a statement, her parents Ann and Jerry said: "The early medical indications were positive as Beth was able to move her hands and feet, despite being in a lot of discomfort.
"The medical staff have been fantastic and explained to us that Beth was waiting for an operation as there were more serious cases ahead of her.
"At 8pm GMT last night Beth was taken down for surgery where they took a piece of bone from her hip and used it to fuse the two vertebrae that were fractured, along with pinning them together.
"It was a scary time for all of us and we're just very grateful that the operation was a success."
Speaking from her hospital bed in Austria, Tweddle added: "Thank you so much for your support and concern.
"The last 48 hours have been very scary but all the messages have really helped to keep me positive. I will keep you updated on my progress."
She became the third member of this year's celebrity contestants to pull out of the Channel 4 show - but more have sustained injuries.
Fellow Olympian Rebecca Adlington, 26, withdrew from the show on medical advice after a shoulder injury. She told host Davina McCall the fall was ''literally the worst thing that has ever happened to me, it was worse than childbirth''.
Holby City actress Tina Hobley, 44, also headed for the exit after she dislocated her elbow and suffered two fractures to her arm.
Sunday night's episode saw contestant Linford Christie, 55, unable to take part in an event due to pulling his hamstring, but he has not ruled himself out of the show.
Meanwhile, former EastEnders star Sid Owen and Made In Chelsea's Mark Francis Vandelli were unable to perform the air jump live due to injury.
Adlington will be replaced by former contestant Heather Mills, who was knocked out in the first round in 2014 and was forced to compete in an unfamiliar prosthetic limb after breaking hers during training.
Hobley has been replaced by The Wanted's Tom Parker. A replacement for Tweddle has not yet been announced.
Ex-EastEnders actress Louisa Lytton became the first contestant to be ski-booted out of The Jump as the latest series of the reality show got under way on January 31.
The Only Way Is Essex (Towie) star James Argent was eliminated on Sunday night.
A Channel 4 spokeswoman said: ''The health and safety of the competitors is always paramount and Beth was immediately taken to hospital for treatment after hurting herself during training.''