The 23-year-old cannot move his legs and has suffered an "incomplete paraplegia" after the accident which happened during training on the Kulm hill in Tauplitz, they told reporters.
"At the moment he cannot move his legs, although he has some sensitivity," Franz-Josef Seibert, chief surgeon at the University Hospital in Graz, told reporters. Seibert added that it was too early to comment on Mueller's long-term prospects.
Sky flying is a version of the Olympic sport of ski jumping, but held on bigger hills and involving longer jumps.
Mueller, junior world ski-jumping champion in 2009, lost his balance and crashed as he was landing after a jump on Wednesday and underwent emergency surgery on his spine.
The championships, which take place every two years, were being held on Friday and Saturday on the same hill, one of the biggest in the world.
(Writing by Brian Homewood in Zurich; editing by Toby Davis)
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