The incident happened in Old Kent Road around 10.45pm on Wednesday (August 27).
The London Ambulance Service says three people were found stabbed and took them to hospital.
One, a 17-year-old boy, is still in a life-threatening condition today (August 29), says the Met Police.
A second 17-year-old boy has been discharged after receiving less serious injuries.
The condition of the third victim has not been able to be verified by the police.
Officers chased and arrested a 17-year-old boy on suspicion of attempted murder.
He has since been released on bail as enquiries into the incident continue.
Old Kent Road has since reopened to traffic.
In an updated statement, a Met Police spokesperson said:
“Police were called at 22.47hrs on Wednesday, 27 August to reports of a stabbing on Old Kent Road.
“Two boys, both aged 17, were found at the scene with stab wounds. One remains in hospital in a life-threatening condition.
“The second was taken to hospital where his injuries were deemed not life-changing or threatening. He has since been discharged.
“Following a short pursuit a 17-year-old boy was arrested by officers on suspicion of attempted murder. He has been released on bail while enquiries continue.
“If you have any information that could help police, please call 101 quoting CAD 8387/27AUG. If you wish to remain anonymous, please speak with Crimestoppers on 0800 555 111.
“We understand the concern this incident will cause within the local community. Residents can expect to see an increased police presence in the area over the coming days.”
