Norwegian police have arrested an armed man who stole an ambulance Tuesday and ran down pedestrians in Oslo, including at least one baby, as the motive was not immediately known.

Police said they were searching for a second suspect -- a woman described as having fair skin and wearing a black jacket, around 1.65cm (5 feet 4 inches) and "who appears to be under the influence" -- who was thought to be involved in the incident.

"We have taken control of an ambulance that was stolen by an armed man," Oslo police said on Twitter.

"Shots were fired to arrest the suspect, he is not seriously injured," they added.

"A woman with a pram and an elderly couple were run over or had to throw themselves out of the way" of the stolen vehicle, police added in another Twitter post.

Norwegian news agency NTB said two seven-month-old twins were in the pram, one of whom was lightly injured and being treated in hospital while the status of the other was not immediately known.

Television images showed a pram lying by the roadside, and an upturned traffic sign.

According to TV2, the arrested man was in his 30s.

Witnesses cited by public broadcaster NRK said police shot at the tyres of the ambulance and the driver fired back.

Police had been pursuing the ambulance when it crashed into a gate outside a residential building.

Television images showed a damaged Mercedes ambulance with what appeared to be several bullet holes in the front left door.

The incident took place in a residential neighbourhood in northern Oslo. Students at a nearby school and daycare centre were ordered to remain indoors.

A large number of police officers, some of them heavily armed, were deployed at the scene.

The suspect's motive was not immediately known, police said.