It happened in the Bronx just before 9 a.m. local time on Henry Hudson Parkway West, over Kappock Street near Independence Avenue in Riverdale.
The front portion of the BxM1 bus along with at least one wheel was dangling over the edge.
Debris was knocked into the roadway on Kappock Street.
Authorities were talking to the bus driver at the scene. The driver was not injured.
There were no customers on the bus at the time of the crash.
The bus is now secure. Crews will hook a heavy-duty cable to the bus to pull it back.