The president of the Norwegian swimming federation, Per Rune Eknes, told The Associated Press via telephone that Dale Oen died after suffering a cardiac arrest.
In a statement, the federation said the 100 metre breaststroke world champion was found collapsed on the floor of his bathroom late Monday. He was taken to the Flagstaff Medical Center, where he was pronounced dead.
"We're all in shock," Norway Coach Petter Loevberg said. "This is an out-of-the-body experience for the whole team over here. Our thoughts primarily go to his family who have lost Alexander way too early."
Hospital spokeswoman Starla Collins confirmed the death, but did not provide further details.
Dale Oen earned his biggest triumph in the pool at last year's worlds in Shanghai when he won the 100 breaststroke, a victory that provided some much-needed joy back in Norway just three days after the massacre by right-wing extremist Anders Breivik that killed 77 people — including children at a summer camp.
Dale Oen dedicated the win to the victims of that massacre, pointing to the Norwegian flag on his cap after the finish to send a message to his countrymen back home.
"We need to stay united," he said after the race. "Everyone back home now is of course paralyzed with what happened but it was important for me to symbolize that even though I'm here in China, I'm able to feel the same emotions."
His death dominated the news in Norway on Monday, and Prime Minister Jens Stoltenberg said on Twitter that "Alexander Dale Oen was a great sportsman for a small country. My thoughts go to his family and friends."
The Norwegian team is holding a camp in Flagstaff ahead of the Olympics, and the federation said Dale Oen had only underwent a light training session on Monday, and also played some golf that day. But teammates became worried when the swimmer spent an unusually long time in the shower, and entered his bathroom when he failed to respond to their knocks on the door.
The federation said "they found Dale Oen laying partly on the floor, partly on the edge of his bathtub."
Team doctor Ola Roensen said he immediately began performing CPR until an ambulance arrived.
"Everything was done according to procedure, and we tried everything, so it is immensely sad that we were not able to resuscitate him," Roensen said. "It is hard to accept."
In his last tweet on Monday, Dale Oen said he was looking forward to going back home: "2 days left of our camp up here in Flagstaff,then it's back to the most beautiful city in Norway.. (hashtag)Bergen."
Dale Oen was born in Bergen, Norway's second largest city, on May 21, 1985. He was the second son of Mona Lillian Dale and Ingolf Oen.
He started swimming at the age of 4, and said on his website that the sport "came very easy and natural for me."
He is the second high-profile athlete to die from cardiac arrest recently, after Italian football player Piermario Morosini collapsed on the pitch during a Serie B game for Livorno last month. That incident came just a month after Bolton midfielder Fabrice Muamba also collapsed during a game, but survived.
"It feels unreal that Alexander Dale Oen is no longer with us," Norwegian skiing champion Aksel Lund Svindal, the two-time overall world Cup champion, said on Twitter. "My thoughts go out to his family, friends and his whole team in Flagstaff."
Keri-Anne Payne, the 10-kilometre open water world champion from Britain, said: "Such sad news for swimming."
AP Sports Writers Andrew Dampf in Rome and Pat Horne in New York contributed to this report.