Emergency services were called to the incident, at the intersection of Tirohanga Rd and the Outram-Mosgiel Rd on State Highway 87, about 3pm.
The person was trapped for a time and had to be cut from the vehicle before being taken to Dunedn Hospital by ambulance, police said.
The sole occupant of the vehicle remains in hospital.
Police said only one car was involved and no one else was in the vehicle.
An ODT reporter at the scene said the car appeared to have crossed the centerline, left the road on the right hand side, clipped a power pole before coming to rest on its side.
The crash has blocked both lanes of the highway and traffic was being diverted down Gladfield Rd and along School Rd, police said.
Police remained at the scene late this afternoon.
The road was closed for some time as the Serious Crash Unit completed its work.
Police have asked for any witnesses to the crash to please make contact with Dunedin Police as soon as possible.
Two-vehicle crash on Kilmog
Earlier on Saturday, police were called to a two-vehicle crash on The Kilmog, about 20km north of Dunedin.
A police spokeswoman said the incident happened on the south side of the hill on State Highway 1 about 2.20pm.
She said it appeared no one was hurt.
Both vehicles were off the road and there was no disruption to heavy traffic in the area.
