The 32-year-old from Calgary, whose has battled injury throughout his career, missed Wednesday's downhill and will skip Thursday's super-G at the World Cup finals in Switzerland.
Hudec crashed during super-G training in Austria last week and tweeted a photo of his bruised and swollen back on Wednesday.
Hudec became the first Canadian alpine skier in 20 years to win an Olympic medal last month in Sochi when he finished third in the men's super-G.
Hudec is currently in Munich and will return to Canada with the rest of the team on Friday. He expects to be sidelined from training for six to eight weeks.
"If all goes well with the back I could return to training as early as May," said Hudec. "I'll have more time to prepare for the season and hope to come back stronger."
He said the Olympics inspired him to keep competing.
"To come away from the Games with that experience motivates me to keep going and keep on racing," said Hudec, who had two World Cup podium finishes this season and is ranked eighth in the world in super-G. "I know there's a lot more in me and there are things I want to achieve in this sport. When I'm healthy, that's when I get excited to race so I'm looking forward to building on this season and coming back healthy."