Scotland Yard said that four men and three women have been detained “on suspicion of various offences”.
Officers and the London Ambulance Service (LAS) found a male with a stab wound to the chest.
He was taken to a central London hospital, where he was pronounced dead just before 5pm.
Police are still at the scene and there are currently road closures along Prentis Road. The public are advised to avoid the area.
Police believe they know the identity of the victim, who is in his late teens, and his next of kin have been informed.
Detectives are still in the very early stages of the investigation and trying to find out the circumstances of what happened.
Local MP Bell Ribeiro-Addy said on Twitter: “My thoughts and prayers are with the family of the young man stabbed to death on Streatham High Road this afternoon.
“Arrests have been made and an investigation is ongoing in the area.”
Anyone with information is asked to call police on 101 quoting CAD 5897/10JUNE.