Emergency personnel say one person was hospitalized with life-threatening injuries and three with serious injuries. Thirty-four people were injured in all.
None of those injured was identified, and state police said they did not know how many of the injured were adults and how many were juveniles.
The bus, which was carrying 42 people, was heading back to Philadelphia after a visit to Harvard University. It struck an overpass on Soldier's Field Road in Boston, a major crosstown road, at around 7:30 p.m. Saturday, authorities said. Some passengers were trapped for more than an hour as rescue crews worked to free them.
Over-sized vehicles are prohibited from using that route, where a 10-foot height limit is in place.
State police are investigating whether charges should be filed against the driver.
The Associated Press contributed to this report.