Emergency services were called to the crash at the intersection with the Main South Road on-ramp in Green Island shortly after 2am.
The Christchurch-based truck carrying chilled and frozen goods left the road before rolling down a bank, landing on its side and blocking the south-bound lane of the motorway on State Highway 1.
St John spokeswoman Siobhan Campbell said they were called to the scene at 2.20am.
Two ambulances attended and took the driver to Dunedin Hospital with moderate injuries.
A police spokeswoman said the road remained closed while a crane removed the truck and trailer, and had since reopened.
Emergency services were called to the single-vehicle incident about 2.35am
Siobhan Campbell said two ambulances attended and took two people to Dunedin Hospital with moderate injuries.
A police spokeswoman said the incident did not cause any road blockages.