The 19-year-old woman was found dead at a house of multiple occupancy early on Saturday morning.
Police are now searching for a man, believed to be known to the woman, who was seen fleeing the building shortly before emergency services were called just before 6am.
Armed police and a dog unit have been at the scene on Unett Street, where the building was expected to be cordoned off throughout Saturday.
Forensic specialists have been examining the scene while detectives seized phones and other evidence from the building as they started their murder investigation.
Detective Inspector Jim Mahon, from the West Midlands Police homicide unit, said: “This is a tragic death of a young woman with her whole life ahead of her.
“We are speaking to other residents at the multi-occupancy address and exploring CCTV to understand what has happened.
“We have a suspect who we are keen to speak to, who is thought to be known to the young woman.”
The nature of the woman's injuries has not yet been confirmed.
Anyone with information is asked to contact police online or by calling 101 quoting log number 765 of July 31. Alternatively Crimestoppers can be contacted anonymously on 0800 555 111.