Officials with the organization had no immediate comment on the crash, the Associated Press said.
The foundation's Facebook page said the group was traveling to Harvard to "visit the campus, sit with the office of cultural advancement, followed by a tour of the campus . . . followed by Harvard Square (shopping, eating, site seeing . . . etc. . . .)"
The crash occurred shortly before 8 p.m. Saturday when the bus struck an overpass in the Allston neighborhood.
Massachusetts State Police said the bus crashed into the Western Avenue Bridge on the eastbound side of Soldiers Field Road, by the Charles River.
Authorities said the Calvary Coach bus did not belong on that road, which was not authorized for oversized vehicles, and state police were investigating whether charges were warranted against the driver, who apparently did not see a sign prohibiting the vehicle from taking that route.
Ray Talmedge, owner of the Philadelphia-based Calvary Coach Bus, said his driver was being interviewed by police. Talmedge said the driver, who also drives a school bus, did not know about the road restrictions.
Of the 34 injured passengers, three had serious injuries, state police said. They said late Saturday night they did not know whether the seriously injured were students or adults.
The Boston Fire Department said some passengers were trapped in the bus. Photos on the department's website showed firefighters lifting victims strapped to boards through the roof of the bus, which bears a Calvary Coach logo.
Four people were taken to Brigham and Women's Hospital for treatment, and 19 were taken to Beth Israel Deaconess, according to a Brigham and Women's Hospital spokeswoman. Boston EMS said the victim with life-threatening injuries was rushed to Boston Medical Center. Another victim was said to have been transported to Massachusetts General Hospital.
Contact Miriam Hill
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This article contains information from tje Associated Press and the Boston Globe.