It happened in Greenpoint at Nassau Avenue and Sutton Street.
The driver reportedly had some kind of medical emergency.
Witnesses say they heard a loud noise, and then watched the bus smash into cars as it continued careening down the street.
Witnesses had to kick open the bus door to get to the passengers.
The Metropolitan Transportation Authority says the bus driver and a female motorist were taken to a hospital with non-life-threatening injuries following the crash.
The MTA says in a release that three others, two bus riders and another motorist, also reported injuries but weren't hospitalized.