Hazrat Wali, 18, of Notting Hill, West London, died at the hospital on Tuesday after being attacked on a playground in Tokenham.
A 16-year-old boy was arrested Thursday afternoon in connection with his death, Metropolitan Police said.
He is being held at the South London Police Station after being arrested on suspicion of murder.
Police were called at 4.45pm on October 12 to report a stabbing at a playground in Crane Fordway, Tokenham.
Officers accompanied the London Ambulance Service and found the victim with stab wounds.
He was taken to hospital, but was pronounced dead at 5.45pm. Police say his family has the help of specially trained officers.
An autopsy is scheduled for Friday at Kingston Mortuary.
Anyone with information or footage of the incident is asked to call the police at 101 or tweet Matt CC, referring to 5697 / 12OCT. Crime stoppers can also be provided anonymously by calling 0800 555 111.