Officers arrested the man outside a business on Andersons Bay Rd just after 2pm following a chase.
Members of the public at the scene who are believed to have helped in the arrest declined to comment.
Neighbour Mel Moana said she saw a man jump the fence and run away and saw a car parked across the road was on fire.
A group of nearby workers helped extinguish the car fire.
A fire investigator is on their way to a garage fire, extinguished this afternoon in St Kilda, Dunedin.
"We have extinguished one fire in a garage," he said. "There's not a lot I can tell you really apart from that.
"A fire investigator is heading to the scene.
"But it is a police matter, so you'll get further comment from them."
Three fire crews attended, one from Dunedin, one from St Kilda and one from Lookout Point, the spokesman said.