Detectives were called to Thomas Street, Briton Ferry, at 09:45 GMT on Wednesday after the body was found in a lane behind the street.
South Wales Police said a 44-year-old man had been arrested and remained in custody.
Det Supt Paul Hurley said: "The body has yet to be identified and a post mortem examination has been arranged."
The area has been cordoned off and forensic examinations of the scene are continuing.
A man has been arrested on suspicion of murder after a man's body was found in Neath Port Talbot.