Police and London Ambulance Service were called at 2.18am on Sunday, 4 April, to a seriously injured woman inside a block of flats in Ravine Grove, SE18.
Officers attended and found a woman, believed aged 50, suffering stab injuries. Despite the efforts of paramedics, the woman died around an hour later.
A post-mortem examination took place on Monday, 5 April at Greenwich Mortuary and gave cause of death as a stab wound.
Officers continue to work to inform all next of kin; formal identification awaits.
A 39-year-old man was arrested at the scene on suspicion of murder. He remains in custody at a south London police station.
The woman and the man arrested are believed to have been known to each other.
Enquires by homicide detectives from the Specialist Crime Command continue to establish the full circumstances.
Any witnesses, or anyone with information that may assist police, are asked to call 101 or tweet @MetCC quoting ref 914/04APR.
Alternatively, contact the independent charity Crimestoppers anonymously on 0800 555 111.