The 30-year-old was advised to rest after a high-speed crash in Schladming, Austria.
Alcott had only just returned following a career-threatening leg break two years ago, and the latest injury has been said to have caused "excessive stress" in the plated fracture of her leg.
Alcott wrote on her Facebook page: "This is by no means the end, I have shown my strength before. The timing blows but better now than in a year!"
She added: "On a positive note, the big jolt to my leg may help the old injured [sic] to further heal so I am likely to come back stronger."
Alcott has five top-10 World Cup finishes to her name, with this injury the latest in a string of recent setbacks.
The 60mph accident occurred halfway down the course, according to Eurosport commentator Nick Fellows.
"It was in a technical part of the course," Fellows told Eurosport-Yahoo. "She was caught on the heel of the inside ski at 60mph, or 100kph.
"She came out of the race line and crashed into the safety netting and was thrown 10 feet into the air before landing hard on her back.
"She lay motionless for two or three minutes before the race marshals persuaded her to get on her skis and she skied off the course.
"The racer behind her on the mountain was yellow-flagged for safety reasons. Chemmy looked in considerable pain, but there was clearly no concussion or necessity for the blood wagon (stretcher).
- Sports & Recreation