Emergency services were called to Purneys Road, Eltham, just before 1pm on Sunday after reports of three men having been stabbed.
No arrests have been made and an investigation is underway, the Metropolitan Police reported.
Air ambulance crews and paramedics also attended – with the first paramedics arriving six minutes later, London Ambulance Service (LAS) said.
He added: “We sent a number of resources to the scene, including ambulance crews, paramedics in ambulances, an incident response officer and the London Air Ambulance.
“The first of our crews arrived in six minutes.
“Our teams treated three male patients at the scene before taking them to major London trauma centers by road as a priority.”
The Met said it was awaiting an update on their conditions.
Anyone with information is asked to call 101 quoting CAD reference 3279/03Nov or contact Crimestoppers on 0800 555 111 to remain anonymous.