Detective Sergeant Chris Henderson, of Dunedin, said someone set alight a couch which was sitting outside the lower Stafford St building about 4am.
The fire then spread to two large wooden doors which led to the entrance of a three-storey building which housed flats.
It could have resulted in fatalities: "It was a block of flats with people asleep inside," Det Sgt Henderson said.
A witness passing by told police five to eight male Caucasians were standing around the burning couch. The witness did not see where they went.
Police would like anyone with any information about the fire or who saw anything suspicious in the area to contact them.