Maria Martinsson, a spokeswoman for the Swedish security service, said: "Three people have been taken into custody. They are suspected of preparing terrorist activity and of financing terrorism."
The detainees, all Swedish citizens, were held in raids around the capital, Stockholm.
Earlier, Norway's state security police said they had arrested three people in Oslo on suspicion of funding "terrorist" activities abroad.
Police also raided at least two internet cafes in the capital and took away computer equipment.
"We are looking for evidence," Martin Bernsen, a spokesman for the country's state security police, said.
Those detained will be brought before a court, probably on Friday or Saturday, Bernsen said.
Sweden's security service said their actions had nothing to do with the recent reprinting of Danish cartoons of Prophet Muhammad, which sparked deadly riots in 2006, or with a Swedish artist, who was threatened over his drawing of the prophet last year.
In Denmark, police arrested two Tunisians and a Dane of Moroccan descent earlier this month, accusing them of planning to kill a cartoonist who drew one of the images of Prophet Muhammad.