Dale Oen, 26, won gold in the 100m breaststroke at the World Championships in Shanghai last year and was considered one of his country's best medal hopes at this summer's London 2012 Olympics.
He was found collapsed in a shower at a training camp in Arizona, with officials saying he suffered a cardiac arrest.
Fellow world champion Rebecca Adlington and British breaststrokers Andrew Willis and Michael Jamieson all expressed their disbelief on Twitter.
A shocked Jamieson said he spoke to his Norwegian rival last week and reported him in 'good spirits' after returning to training from a recent injury. He added Dale Oen planned to travel to Scotland after this summer's Games to spend a few days hiking.
“British Swimming wishes to pass on its deepest condolences to the family of Alexander Dale Oen and all our friends in Norwegian swimming following his sudden death in the USA where he was preparing for the Olympics in London later this year," said British Swimming chief executive David Sparkes.
“Dale Oen was a great swimmer and an inspiration to us all and will be greatly missed by everyone in the sport."
Dale Oen also won Olympic silver in Beijing, Norway's first-ever swimming medal, behind Japan's Kosuke Kitajima, who was expected to be his main rival again this summer.
And British Swimming head coach Dennis Pursley said his loss would be felt in every swimming delegation present at London 2012.
“The international swimming family is small and tightly bonded, so it is always difficult when we lose one of our own," he said.
"It is especially shocking in the case of a young, promising athlete in the prime of his life. His memory will live with us for years to come. Our thoughts and prayers are with the Norwegian federation and Alexander’s family and friends.”
Earlier this year Bolton Wanderers midfielder Fabrice Muamba suffered a cardiac arrest while playing in a FA Cup quarter-final against Tottenham while Italian Serie B player Piermario Morosini collapsed and died following a heart attack last month.