The man, in his 40s, was pronounced dead at the scene of the crash in Parkfield Road while the woman, in her 50s, was treated by paramedics before being taken to hospital in Birmingham.
A 22-year-old man has been arrested on suspicion of causing death by dangerous driving and taken into police custody for questioning.
Officers are keen to hear from anyone who saw the collision involving a red Peugeot 207 and particularly anybody with dashcam footage.
Bystanders performed CPR on the man before ambulance crews arrived.
Interactive map shows where crash happened:
A spokeswoman for West Midlands Ambulance Service said: “Upon arrival crews found two pedestrians who had been involved in a collision with a car.
"Bystanders on scene were already administering excellent first aid to both patients.
“One pedestrian, a man, was in a critical condition.
"Ambulance crews commenced advanced life support to him, but despite everyone’s best efforts, nothing could be done to save the man and he was sadly confirmed dead a short time later at the scene.
"The second patient, a woman, was treated for serious injuries at the scene before being taken to the Queen Elizabeth Hospital in Birmingham.”
Parkfield Road was cordoned off at its junction with the A4123 Birmingham New Road for around four hours after the crash.
Sergeant Dean Caswell, from West Midland's Police's serious collision investigation unit, said: "We’re in the early stages of our investigation and our thoughts are with the families of both the man who has tragically died and the woman left seriously injured.
"We are keen to speak to anyone who was in the area at the time and could have important information to assist our enquiries. I would especially ask anyone with dashcam footage to come forward and speak to us."
Buses were diverted and drivers were warned to avoid the heavily congested area until the road reopened at 10.45am.
One man, a worker at nearby Gills Sausage Factory who wished not to be named, said: "I was walking down Parkfields Road to work at about 6.30am and didn't see anything.
"But a co-worker later came in and said someone had been run over.
"I was shocked as soon as I heard about it and was worried if I knew them. It wasn't anyone that worked here."
Another colleague added: "It is a terrible thing what has happened."
Three ambulances, two MERIT trauma teams and two paramedic officer were sent to the scene.
Contact the serious collision investigation unit on email at FL_COLLISION_INVEST@west-midlands.pnn.police.uk, call 101 or Live Chat us via west-midlands.police.uk between 8am and midnight. Quote log number 315 of December 12.