The Olympic swimmer and mum-of-one, 26, is said to have suffered a "nasty fall" during training for the Channel 4 show.
Rebecca, who has also taken part in ITV's I'm A Celebrity, was rushed to hospital in a stretcher after a ski jump went wrong and she landed badly on her shoulder, says The Sun On Sunday.
Now, says the newspaper, her future on the show is in doubt.
In footage posted by the paper, Rebecca is seen attempting the air jump eliminator, before falling badly.
A source who says they saw the accident in Austria says: "Rebecca's fall was incredibly nasty. One minute she was flying through the air, the next she was crumpled on the crash mat, and clearly in a lot of pain.
"It was hard to tell at first what had happened, but it was clear she needed to go to hospital."
Becky - who won double gold at Beijing in 2008 - is said to have been discharged on Saturday night (30 January).
Talking to the newspaper, a C4 spokeswoman confirmed the star might have to pull out depending on how she recovers.
Not giving too much away apart from confirming she'd been in hospital, Rebecca returned to Twitter on Sunday (31 January).
Instead she simply said: "What a day yesterday. Check out the first live show tonight!!! #TheJump @Channel4 7.30pm!"
A follower responded, joking: "Are you still alive? Can you feel your legs? Of all the shows to do! Celeb Masterchef would be much safer y'know!! ;)."
Another fan asked Rebecca if she was okay, to which she responded: "Still smiling."
That's our girl!
Earlier this week, former EastEnders actress Louisa Lytton, 26, was also rushed to hospital after falling during a training session on the slopes.
She had to be fetched from the piste by Mountain Rescue who sped her to Innsbruck Hospital for an emergency CT scan and X-rays.
James Argent, Beth Tweddle, Brian McFadden, Dean Cain, Sarah Harding, Mark-Francis Vandelli, Tamara Beckwith, Linford Christie, Tina Hobley and Sid Owen are also taking part.
See the full celebrity line-up for The Jump 2016:
Copyright: Channel 4
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