"It was looking out for quite a while," Langford said. "After a couple of minutes the cat got closer to the edge and it looked like she was getting ready to go and she just did," fire department spokesman Larry Langford said.
"It went under my car and hid until she felt better after a couple of minutes and came out and tried to scale the wall to get back in."
The cat was not injured, Langford said, adding he was trying to track down its owner.
Elizabeth Thomas, who lives above the unit where the fire started, told local media she was in her apartment when she smelled smoke and became worried.
"I'm sitting there thinking this ain't nobody BBQing, this smells a little bit more like a grease fire or something that's getting out of hand," said Thomas, 49.
She left her apartment and walked outside the building to see smoke coming out of the unit below hers.
Thomas said she didn't see the cat make the leap, but heard everyone around her react to its escape.
"Everybody was like, 'Oh my god, oh my god,' thinking that it might be hurt but eventually we saw it get up and go limping away.
"I'm just glad no one got hurt. Thank god that cats do have nine lives. I hope I got nine," Thomas said.
The fire was put out by 3.25pm (local time) and no injuries were reported, which was confined to one apartment. The cause of the fire hasn't been reported by officials, nor how much damage resulted.
-AP and additional reporting with the NZ Herald