Police were called to reports of a stabbing at a residential address in Trafalgar Road at around 10.20pm on Wednesday, August 27.
Despite the efforts of emergency services, the woman died at the scene from her injuries.
Formal identification has not yet taken place. A post-mortem examination has already been carried out.
A 33-year-old man, believed to be known to the victim, was arrested at the scene on suspicion of murder.
He remains in hospital with life-threatening injuries.
Detective Inspector Mark Franklin, who is leading the investigation, said: “Our thoughts are with the victim’s family, who at this unimaginably difficult time, are being supported by specialist officers.
“We know this incident will cause great concern within the community. While we are confident this is an isolated incident, residents will see an increased police presence in the area.
“If you are concerned, please speak to one of those officers on patrol.”
Detectives are encouraging anyone with information about the incident to report it via 101, quoting 8218/27AUG.
Those who wish to share information anonymously can speak with Crimestoppers on 0800 555 111.
The investigation continues.