A Hato Hone St John spokesperson said the injured person had been taken to Dunstan Hospital in a moderate condition.
Fifteen people were on board the bus at the time but only one is reportedly injured.
A police spokeswoman said they responded to a single-vehicle crash on the Chatto Creek-Springvale Rd highway (SH85) about 9.40am, after a bus hit a power pole.
The road was closed for a period but reopened under stop/go traffic management and a restricted 30kmh speed limit shortly after 11am.
A commercial vehicle team was making their way from Dunedin to investigate the cause of the crash, the spokeswoman said.
The crash affected a power pole and lines company Aurora reported power was initially out to 310 customers in the Chatto Creek, Galloway, Letts Gully, Springvale and Waikerikeri areas.
The ground in the area is frozen, and nearby Alexandra was the coldest centre in the country shortly after 10am, sitting at -1degC.
Sergeant Adam Elder, of Alexandra, said at the scene that the vehicle was heading towards Omakau and the driver had "just lost it on the road in the ice" and had taken a power pole out.
Inquiries were continuing and Sgt Elder believed the road conditions may have contributed to the crash.
A Hato Hone St John spokesman said two ambulances and one rapid response vehicle went to the scene.
Of the 15 patients aboard the bus, 14 were uninjured, he said.
Waka Kotahi NZTA have issued road ice warnings for the area, including on SH 85 between Alexandra and Omakau, and Kyeburn and Alexandra.
