The blast is thought to have caused damage to the offices of Norwegian Prime Minister Jens Stoltenberg and a number of other official buildings.
Initial reports suggested Mr Stoltenberg was unharmed.
At least eight people were injured in the city centre explosion, local media reports. No-one has said they were behind the attack.
Television footage from the scene showed rubble and glass from shattered windows in the streets - smoke was around some buildings. The wreckage of at least one car was in street.
All roads into the city centre have been closed, said the NRK newspaper.
Oistein Mjarum, head of communications for the Norwegian Red Cross, said his offices were close to the blast.
"There was a massive explosion which could be heard over the capital Oslo."
Mr Mjarum said there were fires burning in the 17-storey prime minister's building.
Eyewitness Ole Tommy Pedersen said he was standing at a bus stop about 100m away from the blast.
"I saw three or four injured people being carried out of the building a few minutes later," Mr Pedersen told AP.
He said there was a cloud of smoke billowing from the lower floors.
An NRK journalist, Ingunn Andersen, said the headquarters of tabloid newspaper VG had also been damaged.
"I see that some windows of the VG building and the government headquarters have been broken. Some people covered with blood are lying in the street," Associated Press news agency quoted him as saying.
"It's complete chaos here. The windows are blown out in all the buildings close by."
This a new one. Unexpected bomb targeting high-level government offices... any ideas as to who and why? Nobody has claimed responsibility, but Norway is part of ISAF and has had ~400 personnel in Afghanistan for years now, which may be a factor. Not that Norway is a hotbed of Islamic extremism; it may be of criminal origin or perhaps from some sort of home-grown nutters.
Some injuries, though so far no word on fatalities. Hopefully none.