State police say most of the injuries were minor, but the bus driver apparently was seriously injured and was flown to a hospital.
Turnpike Authority Spokesman Tom Feeney says the crash occurred shortly after noon in the southbound lanes in South Brunswick.
About 50 to 60 people were on the bus when the crash occurred.
Major traffic delays are being reported.
Footage from a WNBC-TV news helicopter shows a white bus upright on the shoulder, the front end heavily damaged and wedged into the rear corner of the trailer. Emergency teams and firefighters are assisting injured passengers.