Police were called to an address in Hadfield House, Ellen Street, Whitechapel, E1 at 8.17am on Sunday, 24 January after concerns were raised about the welfare of a woman at the property.
Officers attended and found a woman, thought to be in her 30s or 40s, who was unresponsive. She is believed to have suffered a number of injuries, including stab wounds.
Detectives believe they know the identity of the deceased and are working to inform next of kin. A post-mortem examination will 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 investigating.
Anyone with information that could help police is urged to call the incident room on 02083453865, quoting ref CAD1612/21 Jan.
Alternatively, information can be provided anonymously to the independent charity Crimestoppers, on 0800 555 111.
