Police were called to Rotton Park Road in Edgbaston, just before 11pm on Friday, to reports that two people had been shot.
One man, in his 20s, was found in a car but was pronounced dead at the scene.
Another man, in his 30s, was found injured at a bus stop, and was taken to hospital where he remains in a critical condition, West Midlands Police added.
Firearms officers arrested a man in his 30s on suspicion of murder just before 12.30am. He remains in custody.
