The parking officers contacted police about 4.20pm on Wednesday, and within minutes, armed police swarmed the area.
A 38-year-old man was arrested for threatening behaviour.
Police were unable to find a firearm at the man’s home, and inquiries into the circumstances of the incident are ongoing.
Dunedin City Council chief executive Sandy Graham said the incident was "absolutely unacceptable".
She confirmed two DCC parking officers were involved in an incident while visiting an address in North Dunedin.
"Threatening behaviour of any kind directed at our staff is absolutely unacceptable.
"Our staff are doing their jobs and deserve a safe work environment.
"Parking officers do their best to ensure issues like illegal parking are managed effectively on behalf of the community.
"To be confronted with an act of aggression like the one experienced by our officers is just not OK and I know the community at large will agree with that.
"Our staff have families who love them and want them to come home safe each night.
"Our people don’t deserve to be abused or threatened just for going about and doing their job."
She said it was fortunate neither officer was injured, but they were understandably shaken and the council was providing workplace support.
