The victim was found wounded in the front garden of a suburban home shortly after 9pm on Tuesday and died in hospital on Wednesday morning.
An 18-year-old man was detained on Wednesday afternoon and remains in custody at a south London police station, the Metropolitan Police said.
Officers launched a murder probe over the death of the man, who was found in Empress Drive in Chislehurst.
A post-mortem examination has yet to take place and the victim has not been formally identified but his next of kin have been informed.
Detective Chief Inspector Tim Wright, of the Metropolitan Police's Homicide and Major Crime Command, said: "We understand that neighbours and people passing through the area witnessed the incident on Tuesday evening.
"We are keen to speak to all witnesses and would encourage them to come forward as soon as possible.
"A young man has lost his life and we are doing everything we can to piece together what took place."
Anyone with information concerning this incident is requested to call police via 101 quoting reference 7419/9Jan or by calling Crimestoppers anonymously on 0800 555 111.
