"Nick Zoricic fell heavily just before the finish in the round of eight, crashing directly into the safety netting and thereafter lying motionless," the federation said. "The medical care from team doctors and Air Glacier followed immediately."
The Canadian team expressed its condolences.
"Our thoughts are first and foremost with Nick's parents and his family," Alpine Canada President Max Gartner said in a statement. "Nick was a very talented young ski racer and a great athlete who was much loved by his teammates and fellow competitors."
Organizers canceled World Cup events for men and women on Saturday, along with the scheduled World Cup Finals races at the same venue on Sunday.
Zoricic has raced on the World Cup circuit for more than three years and was competing in his 36th event. He placed eighth in the 2011 World Championships at Deer Valley, Utah.
Zoricic is the second Canadian skier to die this season.
In January, 29-year-old freestyle skier Sarah Burke died following a training accident on a halfpipe in Utah.
Zoricic was a member of the Craigleith Ski Club in Ontario.
"I can't believe this tragic news. Nick Zoricic has died? I'm sick to my stomach," former Canadian Alpine racer Brian Stemmle wrote on Twitter.
U.S. racer Ted Ligety also posted a message of condolence for Zoricic on Twitter soon after winning a World Cup giant slalom race in Kranjska Gora, Slovenia.
"Skiing is a great sport that gives but it also takes, sad day to lose Nick Zoricic, you'll be missed bud," Ligety wrote.
Grindelwald has been a venue on the skicross World Cup circuit since 2005. The Swiss village beneath the Eiger and Jungfrau mountain peaks was hosting a meet for the fifth straight year.
"We are all very sad. It is unbelievable for us all," Christoph Egger, president of the race organizing committee, told The Associated Press by telephone. "We are an experienced organizer but, nevertheless, skicross is a sport where four racers fight to win a race. In these circumstances there is a risk to fall or risk of injury, and since today we know there is a risk for death."
Egger said it was a "surprise" to see Zoricic's line of flight off the jump, though "we put the fences there because you have to protect the racers for the finish area."
Race organizers will work with FIS and the Swiss ski federation to analyze the accident and course security.
Egger said the process also requires an accident investigation by legal officers from the state of Bern.