The 34-year-old has said this will be the final season of her career, with a focus on the 2026 Winter Games in Milan-Cortina.
"The first examinations on site suggest an injury to the left knee," the Swiss federation added.
It said Gut-Behrami, who won gold in the Super-G event at the 2022 Beijing Winter Olympics, would return to Switzerland "to undergo more extensive medical tests" following the fall on Thursday.
She also won the overall World Cup title in 2016 and 2024.