Emergency services treated the wounded at the scene but none were believed to have severe injuries, a police statement said, adding there were around 20 passengers aboard the tram at the time of the collision.
Images from the scene showed a blue tram that had penetrated a computer store on the ground floor of a four-story building in the centre of the Norwegian capital.
Demolition worker Thomas Larsen, 41, said he was driving down the street on an electric scooter, towards the tram, when it derailed in front of him.
"I hit the brakes.
Three seconds later, I would have been under it," he said. "It is scary that this could happen in the middle of the city."
The crash triggered a massive response by rescue services, cordoning off the area. The building was evacuated, and will be checked for structural damage, police said.
It was too early to say what had caused the collision, a spokesperson for tram operator Sporveien said. "We are going to have to conduct inquiries on site by our specialists," he added.
