The 40-year-old musician and his 20-person crew were stopped by customs officials at Kjetil Airport in Kristiansand ahead of a planned performance at the Hove Festival on Thursday evening.
Police confirmed that "an artist" had been taken to the city centre police station after being caught with a small quantity of narcotics.
"The person who was arrested at Kjevik has been in for questioning. He has admitted to the illegal importation and possession of a few grams of marijuana. He was issued a 12,000 kroner ($2,000) fine and has been released," police lawyer Per Ørnulf Thorbjørnsen told newspaper Fædrelandsvennen.
The controversial rapper was also fined a further 40,000 kroner after police found he was carrying 227,000 kroner in cash, 202,000 kroner above the legal limit.
Despite the unscheduled police intervention, festival organizers said the headline performer would appear on stage at 10.30pm as planned.
Snoop Dogg previously sparked a storm of criticism in Norway when he appeared to smoke marijuana on stage at the Quart Festival in Kristiansand in 2005.