All three had been under surveillance for some time and the arrests had to be brought forward because of fears that details of the operation could be published.
One suspect is a 39-year-old Chinese man who went as a refugee to Norway in 1999 and became a citizen three years ago.
That man, reportedly the leader of the group, and a 31-year-old asylum-seeker from Uzbekistan with a legal resident permit in Norway, were both arrested in Oslo.
The third suspect, a 37-year-old Iraqi Kurd who holds a Norwegian resident permit, was meanwhile arrested in Germany. He will be extradited to Norway.
Norway's security police chief said that three men suspected 'of preparing a terrorist act and who have links to al-Qaeda have been arrested today.'
Norwegian police did not divulge where the suspected planned attacks had been set to take place.
If found guilty of the crimes, the three suspects face up to 12 years in prison in Norway.
The arrests followed a long, international investigation during which time the suspects had been held under close surveillance.
