Emergency services were called to the fatal crash on Summit Rd, near the Victoria Park car park and the Dyers Pass Rd intersection, about 11pm on Wednesday.
Emergency services were still working to retrieve the car on Thursday morning. It is understood the car went 3m down a bank.
St John spokesman Gerard Campbell said three patients were treated and taken to Christchurch Hospital, one in critical condition, one in serious condition and another in moderate condition.
Fire investigators were also at the scene after a small blaze broke out as a result of the crash.
Fire and Emergency New Zealand spokesman Darryl Ball said three crews attended the incident from the Governors Bay, Spreydon and the Christchurch City stations.
Firefighters had to extricate one person from the vehicle.