The 33-year-old, who is trying to become the most successful ski racer of all time, hurt her back during her run in Saturday's super-G in the glitzy Swiss resort.
She made it to the bottom but slumped to the snow after crossing the finishing line and received lengthy treatment at the course.
Vonn later tweeted she had an "acute facet (spinal joint) dysfunction. I got compressed on the 6th gate and my back seized up."
Vonn said she would see how she responded to treatment overnight, but she tweeted again Sunday morning ahead of a second super-G: "Unfortunately I will not be able to race today.
"I am extremely disappointed but my biggest goal this season is the Olympics and I need to take care of myself now so I can be ready for next week, and more importantly, for February."
Vonn finished 24th in Saturday's race, more than a second behind winner Jasmine Flury of Switzerland, who clinched her first ever World cup podium. Another Swiss Michelle Gisin was 0.1 seconds back, ahead of Liechtenstein's Tina Weirather.
Sunday's super-G was subsequently canceled because of bad weather.
America's Vonn has suffered a catalogue of injuries over her career and began last season's World Cup campaign late after breaking her arm in training last December and then suffering associated nerve problems in her hand.
She began this season by failing to qualify for the second run of a giant slalom race in Solden, Austria, and she crashed
in the opening downhill in Lake Louise before finishing 12th
in a second downhill at the Canadian resort. She fell again in a subsequent super-G at Lake Louise.
Vonn is bidding to break Swede Ingemar Stenmark's record of 86 World Cup race wins. She trails by nine and is the most decorated women's ski racer. She is also targeting February's Winter Olympics in South Korea after missing the defence of her Olympic downhill title in Sochi in 2014 following knee problems.
Earlier this week the two-time Olympic medalist told CNN
she would "absolutely not" visit the White House if invited post-Games, but stressed her passion for her country was undiminished.
"Well, I hope to represent the people of the United States, not the president," Vonn told CNN's Alpine Edge.
She added: "I take the Olympics very seriously and what they mean and what they represent, what walking under our flag means in the opening ceremony.
"I want to represent our country well. I don't think that ther are a lot of people currently in our government that do that."
In St. Moritz Friday, Vonn told reporters: "I was asked my opinion and I gave it.
"I mean, it's not necessarily my place to be sticking my nose in politics, but as an athlete I do have a voice."
On the men's World Cup circuit, home favourite Alexis Pinturault won Saturday's giant slalom in Val d'Isere, France, just along the Tarentaise Valley from his native Courchevel.
Pinturault, the Olympic giant slalom bronze medalist, pipped German Stefan Luitz and Austria's Marcel Hirscher.
Hirscher, the six-time World Cup overall winner and slalom world champion, won Sunday's slalom in snowy conditions from Norway's Henrik Kristoffersen and Swede Andre Myhrer in Val d'Isere.