The dog was beaten and will require veterinary treatment for bruising.
The pair's red Holden utility was also badly damaged during the attack.
Joines said the offenders left the scene in a black Nissan vehicle.
Several members of the public witnessed the apparent unprovoked attack and went to the aid of the victims after the offenders left.
"Police are sickened that adult males armed with weapons would attack a young person at any time and are determined to identify the offenders," Joines said.
"We are asking any members of the public who may have witnessed the events near the intersection with Main and Princess Streets yesterday afternoon to contact us.
Anonymity will be guaranteed."
Palmerston North councillor Adrian Broad said he was concerned the incident happened in a city that was "seen as and known as a safe city in New Zealand".
"Hopefully the police will be on to this and we will catch the offenders quickly," he said.
"These things can happen in any city, but we don't want sort of that negative publicity, do we? It's not good for out city."
Councillor Gabrielle Bundy-Cooke believed there was "more to it than meets the eye".
"It's not something that normally happens in Palmerston North. As I say, I believe there must be more to it.
"It's certainly not what we want to see happening in Palmerston North, not in our city anyway. We're trying to really promote a positive place."
People with information are asked to call the Central District Police on 06 351 3781.
Alternatively, information can be given anonymously to Crimestoppers on 0800 555 111.