Police were called to Hadfield House, Ellen Street, E1 just after 8am on Sunday 24 January after worries were raised about the well-being of a woman at the property.
The police found an unresponsive woman at the address, she is believed to have suffered a number of injuries, including stab wounds. The woman is thought to be in her 30s or 40s.
Officers performed CPR until London Ambulance Service paramedics arrived but despite their best efforts, the woman was pronounced dead at the scene.
It is understood that detectives believe they know the identity of the deceased and are working to inform next of kin. A post-mortem examination of the body is to be scheduled in due course.
A man, believed to be aged in his 30s, was arrested near the scene on suspicion of murder and is in custody at an east London police station.
The deceased and the man arrested are believed to have been known to each other.
Detectives from Specialist Crime (Homicide) are on the case and investigating.
Anyone with information that could help police is urged to call the incident room on 02083453865, or call 101/ tweet @MetCC quoting ref CAD1612/21 Jan.
Alternatively, information can be provided anonymously to the independent charity Crimestoppers, on 0800 555 111.