"I just want to say thanks very much for his quick actions, well done," Te Ura said.
The man had since slipped back into the crowd and disappeared.
The entire float was stopped from carrying on in the parade and police quickly cleared people on the float and the public away from the area.
It happened at the Three Lamps end of Ponsonby Rd, before the parade was in full swing.
Te Ura said the problem seemed to have been caused by the car's engine overheating from moving so slowly.
It was definitely the vehicle rather than the float which was on fire, he said.
A spokeswoman for Air NZ said none of their staff had been injured in the incident.
"A small fire broke out in the engine of the vehicle towing the float.
"The fire was quickly extinguished and around 200 Air New Zealand staff, friends and family continued to march in the parade.''
Mekong Baby restaurant manager Ash Visvanathan said people had seen smoke out on the road but didn't think anything of it at first.
"There was a lot of smoke but I thought it was part of the act," he said.
"Then someone was like no, it's actually on fire."
Two or three people ran into the restaurant asking for fire extinguishers, Visvanathan said.
"They took three and just doused the car."
He said the fire was out pretty quickly and people didn't appear to be too alarmed.
Police had done a good job of moving people away from the scene quickly once they arrived, he said.
Watching the Parade from side was James Matheson, who saw the whole thing unfold.
"We were here, the vehicle caught fire," he said. "There were flames coming out from underneath the vehicle."
Matheson said after a short delay while the fire was being put out other floats just passed by the side of the stopped float.
A regular Parade attendee, he said the night had been great this year despite the minor hiccup.
Shane Olsen of Grey Lynn fire service said it wasn't immediately clear what had caused the fire but the issue appeared to be electrical.
He said the vehicle's driver hadn't realised his truck was on fire until an official pointed it out to him.
"One of the traffic control officials and told him 'hey your car's on fire do you want to get out?'"
Fire services were waiting for the tow truck to arrive before leaving the scene.
