The body of the 36-year-old was found in Monmouth Road, Bartley Green, by ambulance crews, who called police.
Det Insp Warren Hines said it was "believed the deceased and the man arrested were known to each other".
The 51-year-old man is being questioned by police. The house remains cordoned off for forensic investigations.
Anyone with information about the incident was asked to call West Midlands Police.
A post-mortem examination will take place at a later stage to establish the cause of death, a force spokesman said.
A man has been arrested on suspicion of murder after a woman's body was found at a house in Birmingham.