The accident happened around 2:30 p.m. in the eastbound lanes of Route 3 between Passiac Avenue and Main Avenue, with the bus ending up stuck on top of the concrete divider.
Police say eight people suffered minor injuries in the accident. They were taken to two area hospitals.
A crane had to be brought in to lift the bus off the divider.
Police say a car may have cut off the bus while trying to exit.
Clifton Sgt. William Frank says there were 28 people on board, including the driver. Passengers who were not hurt were transferred to another bus.