Police were called shortly before 3am on Sunday, 23 May to reports of gunshots in Consort Road, SE15.
Officers, including firearms officers, attended along with London Ambulance Service. They found a woman, thought to be in her 20s, suffering with a gunshot injury.
The woman remains in hospital with life-threatening injuries.
Detectives from the Met’s Specialist Crime Command (Trident) are leading the investigation.
There is a significant police presence in the area as enquiries continue and a number of roads are currently closed.
At this early stage, there have been no arrests.
Detective Chief Inspector Jimi Tele said: “We are all hoping that this young woman’s condition improves. Our investigation is in its early stages and urgent enquiries are under way to establish the circumstances.
“I would appeal to the residents of Consort Road and the surrounding area to check any doorbell or dashcam footage for any suspicious activity that may relate to this investigation.”
Anybody with information about the incident is asked to call police on 101 or tweet @MetCC quoting CAD 1172/23May. To remain anonymous contact Crimestoppers on 0800 555 111