A spokeswoman at University Hospital in Salt Lake confirmed Burke was being evaluated.
Andy Miller, spokesman at the Park City Mountain Resort, said the accident happened early in the afternoon.
"She was stabilized there at the scene by resort mountain patrol, who took her to base patrol, where she was flown to the hospital in Salt Lake," Miller said.
He said the halfpipe was the same one where snowboarder Kevin Pearce was critically injured during training on Dec. 31, 2009. Pearce suffered traumatic brain injuries but has since recovered and returned to riding on snow last month.
The Canadian freestyle team sent a Twitter message Tuesday afternoon saying Burke, from Squamish, B.C., had a "serious injury." A spokesperson for the Canadian Freestyle Association said there was no additional information yet on her injury.
Burke's husband, Rory Bushfield, also put out a message on Twitter seeking someone with a private jet who might help him and Burke's mother expedite a trip from Vancouver to Salt Lake City.
On the Internet, well-wishers flooded Burke's Facebook page or posted on Twitter, wishing her a speedy recovery.
"@sarah_j_burke - I love you, I'm thinking about, I'm even praying for you," posted Montreal freestyle skier Maude Raymond on her Twitter account.
Canadian snowboarder Spencer O'Brien posted: "Hoping and praying the best for @sarah_j_burke."
"@sarah_j_burke You are strong, please pull through! We all love you and are thinking of you!" posted American superpipe skier Angeli VanLaanen.
Burke was born Barrie, Ont., and grew up in nearby Midland before moving to Squamish. She's a four-time Winter X Games champion in skiing superpipe — a replica of snowboarding's halfpipe on skis. She lobbied aggressively to have the discipline included in the Olympics and was considered one of the top women's voices in the action sport's scene.
With the help of her lobbying, skiing halfpipe will make its debut at the Sochi Games in 2014. If healthy, she is expected to contend for a gold medal.
A few weeks before the 2010 Olympics, while she was still struggling to get her sport included, Burke conceded in an interview with The Associated Press that it was frustrating to be on the outside looking in.
"I think we're all doing this, first off, because we love it and want to be the best," Burke said. "But I also think it would've been a great opportunity, huge for myself and for skiing and for everyone, if we could've gotten into the Olympics. It's sad. I mean, I'm super lucky to be where I am, but that would've been pretty awesome."
Burke was named the Best Female Action Sports Athlete by U.S. sports network ESPN in 2007.
Burke missed significant time in 2009 when she landed awkwardly and broke a vertebrae in her lower back. Since healing, she has returned to the top of her game and was scheduled to defend her title at the Winter X Games later this month in Aspen.
— With files from The Associated Press