The American, the standout name in women's Alpine skiing, announced the news on her Facebook page.
"I am devastated to announce I will not be able to compete in Sochi," said Vonn, the girlfriend of world number one golfer Tiger Woods.
"I did everything I possibly could to somehow get strong enough to overcome having no ACL (anterior cruciate ligament) but the reality has sunk in that my knee is just too unstable to compete at this level."
Vonn, a four-times overall World Cup champion and gold medallist at Vancouver in 2010, badly injured her right knee in a world championship super-G in February and the 29-year-old's return to the slopes has been slowed by setbacks.
She injured her knee again while training for the season-opening World Cup downhill at Beaver Creek, Colorado but appeared to be back on track after racing at Lake Louise, Alberta.
Vonn then travelled with the U.S. team to Europe and again injured her knee in Val d'Isere, France.
"After the incident in Val d'Isere an MRI showed an MCL (medial collateral ligament) sprain, which coupled with the torn ACL, has made it impossible to stabilise her knee and be ready to safely ski again next month," Vonn's public relations team said in a statement.
"She will have surgery shortly and is expected to make a full recovery in time for the 2014-15 World Cup season and the 2015 world championship."
(Photo: Lindsey Vonn poses with the gold medal she won in Vancouver in 2010)