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A police spokeswoman said they received reports of the crash about 7am after a vehicle hit the bridge over the Taieri River, on SH1, and rolled.
The vehicle was not in the water, she said.
St John spokesman Gerard Campbell said two patients were taken to Dunedin Hospital with minor injuries.
Acting Senior Sergeant Anthony Bond said it was a van heading for Queenstown and was full of carpet, as the two male occupants were carpet layers.
The van went onto the bridge heading south, in Allanton-Waihola Rd, when the driver lost control due to snow and ice.
The van crossed to the other side of the road, hit the barrier and flipped, before falling a five metre drop and landing by the river, he said.
The two occupants got out of the van, but were taken to hospital as a precaution.
The road was being swept and would be open shortly with speed restrictions in place, he said.
"Motorists are reminded to drive to the conditions and only travel if it is essential."
The NZ Transport Agency have a warning in place for the area advising motorists to take extra care due to the wintry conditions.