The crash happened during an event at the speedway in Templeton, near Christchurch, about 7pm Saturday.
The rest of the night's scheduled racing was cancelled after the crash.
On its Facebook page, Ruapuna Speedway said the driver suffered burns from fuel igniting during the crash.
It said the driver underwent surgery on Sunday night and was being transferred to Middlemore Hospital in Auckland.
He was in a serious but stable condition.
"We have initiated a full investigation into this freak accident to gain a better understanding of what happened.
"Our thoughts remain with the driver and his family, and we are providing support where possible."
The speedway said anyone struggling with what they had seen at the event should seek help and talk to someone who could offer support.
"Please remember, this was an abnormal accident and not typical of speedway racing.
"We will provide further updates as more information becomes available."
The post said the driver's family had expressed their heartfelt thanks for the support and kind words from friends and the speedway community.
The family also asked for privacy as they focused on the driver's recovery.
A police spokesperson said any investigation into the incident would likely be led by WorkSafe.
On Saturday, Hato Hone St John said it sent an ambulance and rapid response vehicle to the scene on Hasketts Rd.
