The police sent four armed officers to a street near the city centre just after ten on Thursday morning, after receiving reports of an armed man in the area.
The man, who was shot in both the thigh and the back, is now being treated at the nearby University Hospital of North Norway.
Witnesses told VG that police had shouted "Get down! Lie down!" before the shots were fired.
"We received information that there were one or more armed people in the area, and therefore permission was given to sent out armed police," Einar Sparboe Lysnes, from the local police explained.
He refused to be drawn on the reason why police had opened fire.
"I will not say anything about the incident and why it was necessary to shoot," he said. "For the police to fire shots, we must be talking about a situation where with we or others are in danger."
The injured man was known to the police, he added.