The boy was being pushed along the High Street pavement by family when a BMW crashed into another car and then into the pram at around 4pm on Easter Sunday.
The youngster was rushed to hospital but could not be saved.
A relative suffered a shoulder injury but nobody else was injured in the crash.
Meanwhile the BMW driver left the scene but a 34-year-old man suspected of being behind the wheel was arrested in Bloxwich shortly afterwards, West Midlands Police said.
The suspect was taken into custody to be questioned on suspicion of causing death by dangerous driving.
High Street was cordoned off in the aftermath of the crash as collision investigators examined the scene opposite Aldi.
The white BMW 1 Series ended up on the pavement next to Nannza Pizza and Retribution Tattoo, while the Ford B-Max was left on the road with major damage to the driver's side.
Both cars sustained major damage, while the pram was left trapped between the BMW and a wall.
The road reopened at around 9pm.
Sergeant Mark Crozier, from West Midlands Police, said: "A baby has tragically died and we'll be doing all we can to support his family during this deeply devastating time.
"We're in the process of speaking to witnesses and establishing the circumstances around this collision. I would ask anyone who was in the area, and has information which can assist our enquiries, to come forward.
"We understand the shock this will have caused but I would ask people not to speculate on what happened."
Officers are particularly keen to hear from anyone who was in the area and may have dash-cam footage, either before or at the time of the collision.