West Midlands Police said nothing could be done to save the 26-year-old, who had significant head injuries when found by a relative at around 6.30pm on Monday at his home in Scott Road, Olton.
A 34-year-old man was arrested on Friday from an address in Sandwell and remains in custody for questioning.
Detective Inspector Jim Mahon, from the force's homicide team, said: “My thoughts remain with the family and friends of the man who sadly lost his life. They have been fully updated with this latest development.
"Our investigation continues and I’d urge anyone who may have information, but not yet contacted us to get in touch."
Anyone with information should contact police via live chat on our website or call 101 quoting log number 3778 of June 7.
West Midlands Police declined to say where in Sandwell the arrest took place.