The person spoke to The Associated Press on condition of anonymity because an announcement was scheduled later Sunday.
Dr. William Sterett, a physician for the U.S. ski team, operated Sunday on the four-time overall World Cup champion in Vail, Colo.
Vonn tore her anterior cruciate and medial collateral ligaments last week during the super-G in Schladming, Austria. She also broke a bone in her lower leg.
Sterett said earlier he wouldn't set a return date to skiing for Vonn until some time after the surgery. But other doctors believe she could be sidelined for up to eight months.
That would give her time to get back to the slopes for the 2014 Sochi Winter Games, which are a year away. Vonn said recently she intends to defend her Olympic downhill title from the 2010 Vancouver Games.
She was hurt last Tuesday when was lifted into the air off a jump in the opening race at the championships. Upon landing, her right leg gave way and she spun down face first, throwing an arm out to protect herself. Vonn ended up on her back as she smashed through a gate.
She received medical treatment on the snow before being airlifted by helicopter to a hospital in Schladming. A few days, later she flew home to Vail.
This has been a difficult season for Vonn. She took a break for month from the World Cup circuit to regain her strength from an intestinal illness that struck in November. When she returned, she looked like the Vonn of old as she steadily regained her form and won two races last month. Her win in the giant slalom at Maribor, Slovenia, on Jan. 26 was the 59th victory of her career. She's three away from tying the women's record held by Annemarie Moser-Proell of Austria.
While her primary goal is to be ready for Sochi, Vonn ideally wants to be back for the World Cup speed races in Lake Louise, Alta., in late November or early December. She's been so successful there — winning 14 times — that it's become known as "Lake Lindsey."
Comebacks are hardly new for Vonn, who has been plagued by injuries at her last six major championships — from a thumb she sliced on a champagne bottle at the 2009 worlds in Val d'Isere, France, to a bruised shin that she treated with the unorthodox remedy of Austrian cheese at the Vancouver Olympics.
AP Sports Writer Andrew Dampf in Schladming, Austria, contributed.