A spokesman for Norway's skiing association said Svindal, his country's flag-bearer at the opening ceremony, was suffering from allergies and had made the decision after Monday's training.
The 31-year-old was expected to be one of the stand-out performers in Sochi having led the overall World Cup standings for much of the season and now lying second behind Austrian slalom specialist Marcel Hirscher.
But he failed to claim a medal in three races. He was fourth in the downhill, which he had been favourite to win, eighth equal in super combined and seventh in super-G. He will not compete in the Wednesday's giant slalom and Saturday's slalom, neither of which are his forte.
"His shape is not 100 percent, so the best idea is for him to go home and prepare for the rest of the World Cup," Espen Graff, spokesman for Norway's skiing association, said.
"He was prepared well enough to be a medallist in the super-G and the downhill. But he is suffering from some allergies and the doctors are trying to find out what the problem is."
The spokesman added that although Svindal was suffering from allergies similar to spring-time pollen issues, that was not the reason the 31-year old twice overall world champion struggled at the Games.
Svindal is one of a number of favourites who have under-performed in the Olympic Alpine skiing, including American Ted Ligety who has also failed to win a medal.
Little-known skiers such as Switzerland's Sandro Viletta and his female team-mate Dominique Gisin have been crowned surprise Olympic champions.
Svindal has also been eclipsed in Sochi by his team mate Kjetil Jansrud, who earned bronze in last week's downhill before storming to gold in the super-G.
"I came to these Olympic Games as the favourite for two golds. I did my best, but this time I wasn't good enough," Svindal said on his facebook page on Sunday.
"These Olympic Games where not my championship. But I'm lucky to have awesome team-mates that can step up when I fail."
In Vancouver four years ago, Svindal won Olympic super-G gold, downhill silver and giant slalom bronze.
After Sunday's super-G, Norway's head coach Havard Tjorhom said: "That was probably one of his best chances but we want to attack also in the giant slalom. We're looking forward to that."
Svindal has won five gold medals at world championships and is the reigning world downhill champion.
Up to the Games, his form this season had drawn praise across the board, prompting Kjetil Andre Aamodt, Norway's most-decorated ski racer, to declare: "He has been outstanding - all the rest are just extras."
But Svindal has bounced back from setbacks before and tweeted on Tuesday: "if every day was the same you wouldn't really learn much. Wins and defeats. I put them both in my 'life experience' account."