Gut, who won bronze in the worlds' opening super-G, was airlifted to hospital after rupturing the anterior cruciate ligament and tearing the meniscus of her left knee during the warm-up for the slalom run of the alpine combined event.
The 25-year-old confirmed on social media that "last Monday I had surgery on my left knee".
Dr Olivier Siegrist has "reconstructed my ACL and my torn menisci have been sutured", she said.
"I just want to say a big thanks to him and the entire team at the Hopital de La Tour in Geneva, to my physiotherapists, my team and every single person which has helped me going through those days."
In Gut's absence, the Swiss team rallied to finish second in the medals table at the world championships behind Austria, having won three golds, two silvers and two bronzes.