An Austrian Ski Federation statement said Morgenstern's injuries were not life-threatening.
The 27-year-old lost his balance in the air, turned over and landed on his back and head, the FIS said on its website.
He briefly lost consciousness but was able to speak shortly after the crash at the ski flying event in Bad Mitterndorf, Austria.
Ski flying is a form of ski jumping from a higher slope so that the skier jumps further.
Austria's team doctor Herbert Leitner said: "Fortunately he was responsive, Thomas can move (his) arms and legs. That's very important. He asked me what happened."
Morgenstern received first aid on the hill and was flown by helicopter to a hospital in nearby Salzburg, where he is in intensive care.
"We can only hope for the best," said Alexander Pointner, the team's head coach. "This really hurts because we are all very close. Thomas is the heart of this team."
It is the second heavy fall for Morgenstern this season, with the Sochi Olympics only a month away, after he crashed on the snow following a jump at the World Cup in Titisee-Neustadt, Germany, on December 15.
Then, he suffered several bruises, face cuts and a broken finger but recovered quickly and finished runner-up to fellow Austrian Thomas Diethart in the Four Hills Tour last week.
Morgenstern won two Olympic titles in the individual and team large hill event in Turin in 2006 and a team large hill gold in Vancouver in 2010.
- Sports & Recreation