Vonn, 42, said before the procedure that surgeons would remove almost all the rods and pins that were inserted in the eight previous surgeries to rebuild her anterior cruciate ligament.
In a video she uploaded on social media, Vonn said: "This will be my ninth surgery and I'm praying my last.
"There are still things that could change in surgery, so we will have to wait and see how it goes."
Her exit several seconds into her race at the Milan-Cortina Games came after she had suffered torn knee ligaments in her left leg following a crash during the build-up to the Olympics.
After being airlifted off the Olympic piste, Vonn underwent a series of operations in Italy to repair her leg before returning to the United States, where she underwent a further procedure to prevent the limb from being amputated.