West Midlands Police said the victim, who was in his 40s, was struck on Birmingham Road, West Bromwich near to The Hawthorns, just before 9pm on Saturday.
He died at the scene, with his family informed and supported by officers.
The force said the driver initially stopped at the scene, then left.
However, an arrest was made in the early hours of Sunday morning, while a car has also been recovered.
A police spokesperson said: “At around 5am today, a man aged 64 was arrested in Birmingham on suspicion of causing death by dangerous driving and driving while unfit through drink.
“He remains in custody today. A Mitsubishi car has also been recovered as part of the investigation, and the road has now been re-opened.”
Anyone with information, dash cam or CCTV footage has been asked to get in touch via Live Chat or 101, quoting log 4352 of 5 October.
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