Police have not yet identified the victims of the crash, which occurred shortly before 3am on Wednesday.
The accident took place on national road 159 after the car passed through a tunnel near the town of Rælingen.
“We suspect the car was travelling at high speed,” said police investigator Bjørn Jahr.
“It came out of the tunnel and continued towards the river. It looks like it may have hit a section of the bridge and then ended up in the Nitelva river.”
There were no witnesses to the accident, but locals reported hearing a loud bang.
Police officers arriving at the scene found car parts strewn over the road, at the side of the road and in the water.
Police divers found the car and the two bodies some 15 metres from the riverbank at 3.30am.