Norwegian police said two of the individuals were apprehended in Oslo, Norway's capital, and one was apprehended in Germany with the co-operation of the German police.
'Links to New York plot'
Jan Glent, the national prosecutor, said the three had been "charged with having entered into a partnership to commit a terrorist act".
"We also think they have links to al-Qaeda and to similar attempts [at attacks] in New York and Manchester," he said.
Police told the Reuters news agency that the arrests were brought forward over fears that details of the investigation would appear in public.
"We are seeing developments in Norway that resemble conditions in countries where acts of terror have taken place"
Norwegian prime minister
"We were afraid evidence would be destroyed, because we knew that an international media organisation was about to publish details of the case," Kristiansen said.
"That made it urgent to make the arrests."
The action came a day after US prosecutors named senior al-Qaeda leaders as being behind a plot foiled last September to set off explosions in the New York
Prosecutors also said one of the men was linked to a bomb plot in the northeastern English city of Manchester last year.
Kristiansen did not say which country was the target of the planned attack, but said the "terrorism" threat to Norway remained minor.
Jens Stoltenberg, the Norwegian prime minister, described the arrests as "the most serious" of their kind to have been made in the country.
"We are seeing developments in Norway that resemble conditions in countries where acts of terror have taken place," he said.
"We have to be on our guard."
If found guilty of the crimes, the three suspects face up to 12 years in prison in Norway, where prison sentences tend to be short.