Authorities said four of the injured were listed in critical condition, while another 12 were in serious condition, ABC News reported.
Passenger Christopher Lake said the bus started shaking, then hit a tree and rolled at least twice.
Some 29 people were transported to area hospitals, WKRC-TV in Cincinnati reported.
The bus was northbound on Interstate 75 from Cincinnati to Detroit, Mich., when the accident occurred about 4 a.m. in Butler County.
Police shut down both sides of the highway for a time after the accident.
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