Detectives launched a murder inquiry following the attack on the bus on the Hagley Road leading out of the city.
The victim died at the scene.
A suspect was earlier detained in connection with the stabbing but has now been released, West Midlands Police said.
They have launched a manhunt for a black male in his late teens or early 20s.
"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."