Naomi Hunte, 41, was found dead after police were called to an address in Congleton Grove, SE18 at 8.25pm on Monday, 14 February.
A post-mortem examination took place on Wednesday, 16 February at Greenwich Mortuary and gave cause of death as a stab wound.
A 63-year-old man was arrested on suspicion of murder today (Friday, 18 February). He has been taken into custody.
Anyone with any information about the murder is asked to contact the incident room on 020 8721 4027
Alternatively, call police on 101 or tweet @MetCC and quote CAD6610/14Feb.
To remain 100% anonymous contact the independent charity Crimestoppers on 0800 555 111.