The man was detained after a body was found in shrubs next to a high-rise flat building in the Heath Town area of the city on Tuesday evening.
West Midlands Police confirmed on Thursday that the 40-year-old suspect had been arrested on suspicion of murder.
On Wednesday the force had said the death was being treated as unexplained ahead of a post mortem being held.
It is believed the 44-year-old man found dead, who lived in Hawthorn House and was known to the suspect, may have been in the bushes for more than 24 hours before being found.
Police and paramedics were called to the scene off Clover Ley at around 5.30pm and the man was soon pronounced dead.
Residents of the city tower block yesterday spoke of their sadness and concern for their children after the incident.
One neighbour, who asked not to be named said: "I'm very shocked and scared about what has happened and don't know what to think about it.
"I hope it doesn't happen again around here as I have children and I really fear for them when things like this happen so close to home."
West Midlands Police has urged any witnesses or anyone who was near Hawthorn House since late morning on Tuesday and who may have seen anything to contact them.
Call the force on 101 or message on Live Chat via their website quoting log 3345 from 9/11.