It appears to have been caused by a faulty front tyre, officials say, adding that the inquiry is ongoing.
The charter bus was taking pupils from Long Island to a band camp when it ran off the road and tumbled into a ditch near the town of Wawayanda.
Officials say 44 people were on the bus. They have been taken to six regional hospitals for treatment.
The crash occurred around 13:10 local time (18:10GMT) on Interstate 84, about two hours north of New York City. Police have closed the highway to allow work tob be carried out at the crash scene.