Detectives launched a murder inquiry following the attack at around 7.30am in Birmingham.
West Midlands Police said officers were immediately dispatched to the scene but were unable to save the victim.
Hagley Road, leading out of city, was closed in the wake of the killing and is expected to stay shut for the rest of the day.
A spokesman said: "At 7.37am today police received a call from a member of the public reporting that a passenger had been attacked.
"Officers and other emergency services were immediately dispatched but it was clear that nothing could be done to save the victim.
"West Midlands Police have identified the victim's family and are in the process of breaking the sad news."
West Midlands Ambulance Service said it was called to an emergency on board a bus in Edgbaston shortly after 7.35am.
A spokesman said: "A senior paramedic officer in a rapid response vehicle, two Basics (British Association for Immediate Care) emergency medics and two ambulance crews attended.
"One person was confirmed dead at the scene."