Cheshire, just 18, is the second-youngest member of the 56-strong GB team in Sochi but is considered a medal chance after becoming the first British woman to win a ski World Cup gold in 24 years last month.
Olympic organisers confirmed she fell heavily on her face and, after remaining unconscious for several minutes, was taken on a stretcher to a nearby medical tent.
Team GB officials said she was then taken from the course to the polyclinic in the athletes' village, where she is being evaluated by their own staff, headed by chief medical officer Niall Elliot.
Cheshire is due to make her Olympic debut on Thursday and had started official training on the halfpipe at the Rosa Khutor Extreme Park last Friday.
Team officials said it was too early to state whether she would be fit to compete but, speaking last week, Cheshire was looking forward to being in medal contention.
"I thought I could probably fly under the radar but I suppose what happened in the World Cup changed a lot of things," she said. "In a way it puts more pressure on me, more people seem interested in me now, which is also a good thing.
"At the start of last year just being here probably wasn't really a possibility and I need to remember that I've got more Olympics ahead of me. I think since last summer I've come into competitions all guns blazing with lots of new tricks and people are looking at me a bit differently. Maybe I scare them a little bit, which is a good thing.
"I'm going to push my runs and get as many tricks down as I can and hopefully that could get me on the podium."
Elsewhere, Swiss aerials skier Christopher Lambert was taken to hospital after suffering a suspected dislocated elbow while Russian ski cross athlete Maria Komissarova underwent a six-and-a-half hour operation after breaking her spine during training on Saturday.
Cheshire's injury also came at the end of a day in which two heavy crashes delayed the women's snowboard cross event with Norway's Helene Olafsen and American Jacqueline Hernandez stretchered off the course after accidents in the seeding run.
Great Britain's Zoe Gillings finished ninth and did her best to sound upbeat after losing out on an Olympic final place following a photo finish.
Gillings and Italian rival Michela Moioli rolled across the line on their backsides after both fell within sight of the finish in their semi-final in Rosa Khutor. Unfortunately for Gillings, Moioli rolled just that little bit quicker.
It meant she was left to settle for ninth place on her third Olympic appearance and to reflect on what might have been, following her 15th in Turin and eighth four years ago in Vancouver.
And it would not be snowboard cross - in which six riders race each other down a course punctuated with lumps, bumps and jumps - without some drama from American Lindsey Jacobellis.
She wrote her name in sporting folklore by pulling a showboating trick within sight of the finish line at the 2006 Games - and falling flat on her face to lose gold, the ultimate example of sporting hubris.
She was well clear of her rivals again in Gillings' semi-final, only to catch an edge and fall, which promoted the British snowboarder into a qualifying place but also forced her to slow down.
She came across the final jump neck and neck with Moioli but both fell again in their desperate attempt to make the top three. "I'm really disappointed about the photo finish and not quite making the final but it can be pretty small margins in this sport. One of the officials said I'd made it but it flashed up on the screen about 15 seconds later that I hadn't," she said.
"Lindsey fell in front of me and I had to change my line and that cost me some speed and is probably why I got caught on the line.
"There are crashes in snowboard cross and you have to deal with it and concentrate on what you're doing. It's a big course but it needs to be big to be challenging, after all people expect that at the Olympics.
"When you are racing you've got so much to think about that you don't have time to be worried."
Gillings said she was aiming to try again for that elusive medal in four years' time. "As long as the funding is there and I'm still enjoying it, there is no reason not to go for another one," she said.