The incident happened near the Greek Meze in Main Road just after 10.40pm yesterday (April 10).
Officers and London Ambulance Service crews attended and found an 18-year-old injured.
He was taken to hospital for treatment where his condition was assesed as critical.
Three people, two men in their 40s, and a 31-year-old woman have since been arrested on suspicion of affray.
They remain in police custody.
A spokesperson for the Metropolitan Police said: “Officers believe many people were present at the time of the assault, who haven’t come forward and spoken to police.
“If you were there and have any relevant information, please contact the Met urgently via 101, quoting 8536/10APR. Anonymous reports can be submitted through Crimestoppers on 0800 555 111.
“Local residents can expect to see an increased police presence in the area as a crime scene remains in place outside a restaurant in Main Road, Sidcup while early enquiries are conducted.”
