The 32-year-old native of Mont-Tremblant, Que., said on his Twitter account that his knee was bothering him. Guay underwent knee surgery over the summer, then returned for the start of the World Cup season after an intensive rehab program.
"Did everything we could but my knee is not in a place where I can push it. Kitzbuehel is a no go," Guay posted on his Twitter account.
Guay is one of Canada's top hopes for an alpine skiing medal at the Sochi Olympics. He has won gold and bronze on the World Cup circuit this season.
He holds the Canadian record with 21 career World Cup medals. That's one more than "Crazy Canuck" Steve Podborski, who will be the chef de mission for the Canadian team in Sochi.
American Bode Miller was the fastest in Thursday's training run with a time of two minutes 2.93 seconds. Conrad Pridy of Whistler, B.C., was the top Canadian in 24th.