The incident began soon after noon in the suburb of Wadestown, after a man allegedly entered a property and threatened the occupants with a long, bladed weapon.
Police were called to a house on Annew Street about 12.35pm, after a report the armed man had attempted to steal a vehicle.
When challenged by police, he started causing damage at the property and pepper spray was used.
Wellington District Commander Superintendent Corrie Parnell said the man retreated to a room in the house and refused to come out.
"While police were trying to de-escalate the situation, the man has become violent and has presented a threat to attending staff, while still in possession of his weapon.
"OC spray and tasers have been used, and when the man has continued to escalate, a single shot has been fired by a police staff member."
Police negotiators and the Armed Offenders Squad were called in, and a police dog was used to help take the man into custody about 2.20pm.
"The man has been transported to hospital to receive treatment for a dog bite, where he will remain under police guard," said Parnell.
"He has also sustained a superficial injury to his shoulder, believed to be as a result of the shot fired."
Parnell said it was a "fast-moving situation involving a volatile offender".
"We are fortunate this incident was resolved with no injury to our staff or members of the public.
"We will be ensuring the victims of the initial burglary incident receive support, as they are understandably very traumatised by what's happened today.
"Our staff attending the incident will also be supported."
He said charges were still being considered.
