Police were called by ambulance workers to an address in Dover Close, Bartley Green, at around 6.20pm on Friday where a man was in cardiac arrest.
The 36-year-old was pronounced dead at the scene. A post-mortem will take place to find out how he died.
A 48-year-old woman has been arrested on suspicion of murder.
Detective Inspector Stuart Mobberley from the force homicide team said: “Our investigation continues to establish the circumstances surrounding this man’s death.
“Every bit of information is vital to our investigation and I would urge anyone who can help to get in touch."
Anyone with information is asked to get in contact via Live Chat at west-midlands.police.uk between 8am and midnight, or call 101 anytime, quoting log number 3970 of 16 October.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org