Police, St John and firefighters were called to the single-vehicle collision at the corner of Selwyn and Coronation Sts in Spreydon about 2.23am.
A St John spokesman said one patient was transported to hospital.
A Fire and Emergency New Zealand spokesman said no one was trapped in the vehicle and crews were there for about 10 minutes before being stood down.
He said the tree was badly damaged and city council staff were going to look at it today to see if it needed to be removed.