The driver, who suffered a gash in his arm, told state police that he was cut off by another vehicle, though it was not immediately clear whether that caused the crash around 7:30 a.m. on eastbound Interstate 80 in Wayne.
Some windows burst during the crash and their frames pinned three people, but they were quickly freed and taken to hospitals with the other injured. The bus had been chartered by a church group.
Eight of the injured passengers were admitted in critical condition, hospital spokeswoman Liz Asani said. Further details on their injuries were not disclosed. The rest of the injured, including two young children, were being treated for minor injuries at two other hospitals.
State police have said none of the injuries are considered life-threatening.
"It was terrifying," Norma Cumberbatch, 66, of Toronto, told The Star-Ledger of Newark. Cumberbatch, who was traveling with her 68-year-old sister, Marjorie, said she struggled to free her legs from fallen luggage and other debris before trying to find her sister.
"I just took my leg out and then said, 'Where's my sister? I want my sister.'"
Marjorie Cumberbatch said she heard "thump, thump, thump. Then I looked up and I saw people over me screaming and crying."
Passengers who were unhurt were put on another bus and continued their journey, authorities said.
The coach bus was from Toronto-based AVM Max 2000 Charter Services Inc., state police said. The phone for AVM Max rang unanswered Saturday afternoon, and the company did not respond to an email Saturday.
The crash was the latest of several coach bus accidents over the past few years on American highways. Last year, a bus carrying gamblers from a trip to a Connecticut casino struck a guardrail as it entered New York City, then toppled over and hit a signpost that sliced off the top of the bus. Thirteen people were killed. A manslaughter trial for the driver began last month.
Saturday's accident backed up traffic in the area for hours while law enforcement officials and emergency services vehicles attended to the scene. Several highways connect there, and the area is known locally as the "spaghetti bowl," according to The Record.