Four people were seriously injured and 36 others suffered minor injuries, a dispatcher for the Broome County Sheriff's Department said.
The accident occurred on Interstate 81 in a southbound lane near Whitney Point, a scenic village of about 1,000 residents. The bus, which appeared to have no markings on its sides, sat in the ditch on its roof with its wheels in the air.
Paramedics were evaluating people, many with neck and chest injuries, at the scene.
At Lourdes Hospital, in Binghamton, about 20 miles south of Whitney Point, clinical manager Barb Anderson said people from the bus were getting X-rays and tests and it was unclear how many would be admitted. There were no young children among the injured, but two patients appeared to be in their teens, she said.
The Syracuse Post-Standard reported some passengers appeared to be trapped in the bus.
The Sun & Press-Bulletin said several people were on the side of the road wrapped in blankets and another was loaded into an ambulance.
The southbound side of I-81 was closed around Whitney Point, Department of Transportation spokesman Dave Hamburg said.
Tour bus industry safety has drawn heightened attention since the March 12 crash of a bus returning to New York City's Chinatown after an overnight excursion to a Connecticut casino. Fifteen people were killed when the bus flipped onto its side and struck a pole, peeling off its roof.
A passenger has said the driver fell asleep; the driver has said he was alert and well-rested. That crash is being investigated by state police and the National Transportation Safety Board.
Since that crash, New York has sidelined hundreds of buses and bus drivers in a stepped-up program to stop buses for safety evaluations. Many drivers were found to have had multiple driver's licenses with histories of violations.
Just days after that deadly crash, a luxury tour bus from New York City's Chinatown to Philadelphia crashed on the New Jersey Turnpike, one of the nation's most heavily trafficked highways, killing the driver and another person. The bus entered the grass along the center median before striking an overpass support and hitting an embankment.
Last month, a fiery crash between a tractor-trailer and a tour bus in upstate New York killed the truck driver and injured at least 30 passengers on the bus.