The accident happened in the southbound lanes just north of Interchange 8A - NJ 32 in Monroe just after noon.
All southbound lanes of the New Jersey Turnpike are closed to traffic at the accident scene.
The bus was traveling from Brooklyn to Washington D.C., and apparently made a stop in Manhattan.
Fifty-three people were on the bus when the crash occurred, said Dan Ronan, a spokesman for the American Bus Association.
While most of the injuries were described as minor, the driver remained in critical condition at the hospital. New Jersey State Police and other officials had earlier said he had died, but then said he remained alive.
The driver is 52 and a professional driver for 11 years, Ronan said. Ronan said his medical certification was current and that he has no violations on his commercial license.
Seven of the injured were taken to Robert Wood Johnson University Hospital in New Brunswick. Two were listed in critical condition. Five were listed in fair condition.
Other injured passengers went to Centra State Medical Center in Freehold and Saint Peter's University Hospital in New Brunswick.
Bus is operated by DC Trails, which is a charter and tour bus company serving the Washington D.C. area.
The accident caused extensive delays on the turnpike and nearby local roads.