Vonn, running first, grimaced in anguish after she nearly missed a gate and struggled to keep her line in her descent of 1min 21:49sec.
The 33-year-old was denied a medal when she was outpaced by Italy's Johanna Schnarf, Switzerland's Lara Gut and finally Tina Weirather of Leichtenstein, running seventh. Forty-five skiers are on the start list.
Vonn, one of the best known athletes at the Games, took super-G bronze along with downhill gold at Vancouver 2010. She will also compete in the downhill and combined.
Her disappointment comes a day after giant slalom winner Mikaela Shiffrin was fourth in the slalom, ending her bid to retain the title she won in Sochi.