Vonn, 41, was flown by helicopter to the Ca' Foncello Hospital in the city of Treviso from Cortina d'Ampezzo after her audacious bid to win downhill gold with a ruptured knee ligament ended in agony on Sunday.
She was operated on by a joint team of local orthopaedic and plastic surgeons, the source close to the matter said on Monday, explaining that the procedures were intended to prevent complications linked to swelling and blood flow.
Vonn's personal doctor was present but only assisted while Italian surgeons led the procedures, the source added.
The United States Olympic and Paralympic Committee did not respond to a request for comment about the treatment for Vonn, one of the most decorated ski racers in history.
The hospital had said she underwent an operation to stabilise her left leg, but did not mention a second procedure.
'One in a thousand' accident
The case has highlighted a debate in elite sport over who decides when an injured athlete is fit to compete and what message those decisions send.
International Ski Federation (FIS) President Johan Eliasch said the competitor had to make up their own mind.
"I firmly believe that this has to be decided by the individual... And in her case, she certainly knows her injuries a lot better than anybody else," he told reporters on Monday.
"And what is also important for people to understand is that the accident that she had yesterday, she was incredibly unlucky. It was a one in a thousand. She got too close to the gate, and she got stuck when she was in the air in the gate and started rotating."
His view was echoed by Pierre Ducrey, sports director of the International Olympic Committee.
"She was able to train and made the choice with her excellent team to take part," he said.
The USA ski team had inspected several facilities before selecting Treviso, some 125 km (80 miles) from Cortina, favouring it over a closer hospital in Belluno because Treviso also has a neurosurgery department, the source said.
Vonn has been inundated with messages of support from the sporting world and beyond.
"You are a great inspiration and an example of perseverance," said tennis great Rafa Nadal. "Stay strong and get well soon!"