Police said they were searching for a second suspect -- a woman described as having fair skin, brown hair and wearing a black jacket, around 1.65 metres tall and "who looks intoxicated".
"We have no information for now indicating that this is terror-related," Oslo police wrote on Twitter.
The man aimed a shotgun at police, stole an ambulance and intentionally drove on to the pavement in an attempt to hit passers-by, NRK reported on Tuesday afternoon.
The broadcaster has reported the following sequence of events.
At around 12:35, police were alerted to an accident at Rosenhoff in Oslo near Sinsenkrysset, where a car was overturned.
When police and ambulance services arrived at the scene, the man aimed a shotgun at police and stole one of the ambulances.
He then attempted to drive into police before driving away in the ambulance. He was pursued by police in the direction of Torshov.
According to witness accounts, there were two people in the overturned car: a man and a woman. The woman left the scene on foot and disappeared for several hours. She is previously known to police.
Three ambulance staff who were in emergency vehicle before it was stolen were not hurt, Oslo University Hospital (OUH) confirmed.
While police were chasing the car, it drove into a woman with seven-month-old twins in a pram. The babies were mildly injured, OUH has also confirmed.
As the ambulance continued through Torshov, and elderly couple were able to throw themselves out of its path. They were subsequently taken to hospital. Police believe the driver intentionally targeted pedestrians.
Officers eventually shot at the ambulance to bring it to a halt. The driver, described as in his 30s, was arrested at around 12:45 and was not hit by any of the shots.
Following the arrest, police found a shotgun and an Uzi semiautomatic machine gun and what they believe to be narcotic substances. The man had previously been photographed carrying a blue tarpaulin bag of the type available from furniture outlet Ikea.
After searching several addresses, police arrested a 25-year-old Norwegian woman. She is suspected of possessing firearms.
Although police have said there are no indications that the incident was a terror attack, they are investigating broadly. The two suspects are known to police to have connections to far-right movements. These connections are now being investigated.
The man is suspected of attempted murder and has been described as 32 years old and from Eastern Norway. He is also previously known to police.
READ ALSO: UPDATED: Norwegian police arrest gunman after stolen Oslo ambulance driven into pedestrians