A Fire and Emergency New Zealand spokeswoman said the crash happened on Oxford Rd in Fernside about 9.50am on Monday.
The truck was carrying a number of golf carts and towing a rally car that appears to have been severely damaged.
They could not say if anybody had been injured. St John has been approached for comment.
A police spokesperson said it appears power lines in the area are down.
Mainpower has indicated about 50 nearby homes were without power.