Constable Reece Munro, of Dunedin, said it appeared a silver Audi travelling north in Leith Valley Rd and carrying four people, failed to stop at a stop sign when it reached State Highway 1 at Pigeon Flat about 2.20pm yesterday.
The car was driven on to the highway, colliding with an Isuzu Bighorn travelling north.
The single occupant of the Isuzu was not injured, but the three passengers in the Audi were all taken to Dunedin Hospital by ambulance - two with minor injuries and one with moderate injuries.
That person was in a stable condition in hospital last night, police said.
Both vehicles were written off in the crash.
A police dog tracked the missing driver of the Audi for some time before losing the trail.
Anyone with information about the driver's whereabouts should ring Dunedin Central Police Station on 471-4800, Const Munro said.