Police were called to Southborough Lane in the early hours of Sunday morning following reports of a collision.
Officers attended with London Ambulance Service paramedics and found a 16-year-old male, who had been riding the e-scooter, with serious injuries.
He was taken to a central London hospital where he sadly died. His next of kin have been informed and are being supported by specialist officers.
The driver of the car involved in the collision, a red Fiat Punto, did not stop at the scene.
It was discovered later the same morning in Southwood Close, Bromley.
The driver, a 20-year-old man, was arrested on suspicion of failing to stop at the scene of a collision, causing death by dangerous driving and providing a positive alcohol breath test. He was taken into custody where he remains.
Officers are also investigating the disappearance of the e-scooter that was being ridden at the time of the collision. It is believed to have been stolen from the scene.
A dark-coloured people carrier type car with a sliding door was seen in the area and officers are keen to speak to the occupants in relation to this aspect of their investigation.
Anyone who saw the collision, witnessed the removal of the e-scooter, or who saw a red Fiat Punto being driven in the area at around 01:20hrs, is urged to call police on 0208 285 1574, providing the reference 775/18JUL.
Information can also be provided to Crimestoppers, anonymously, by calling 0800 555 111.
Local residents are also urged to check doorbell video cameras and drivers who were in the area are asked to look back on dash-cam footage, to see if they have captured anything related to the collision or the vehicles involved.
It comes about a week after the Government faced criticism about private e-scooters with critics suggesting the roads had become “a wild west of lawlessness” since they were allowed.
Ministers had encouraged the “de facto legalisation” of the electric devices, leading to a situation where “riders are terrorising pedestrians”, Parliament was told.
The Tory administration faced a barrage of criticism in the House of Lords over the proliferation of e-scooters, which have fuelled safety concerns and claims that police are “turning a blind eye”.
While freely available to buy and a common sight on roads and pavements, e-scooters cannot legally be used in the UK except on private land.
Only rental scooters are currently permitted to be ridden as part of official Government trials across the country and they are not allowed on pavements.
Pressing the issue at Westminster, Liberal Democrat Baroness Ludford said: “This Government claim to represent the party of law and order, and certainly they often talk about crackdowns, but, when it comes to e-scooters, they have allowed, even encouraged, de facto legalisation without the necessary legislation to protect riders and the public.
“This has caused problems to escalate out of control in a wild west of lawlessness, where riders are terrorising pedestrians, especially those with disabilities and visual impairment.
“The Government have also failed to regulate the sale and use of private ones, which probably number in the hundreds of thousands. Why are this Government refusing to act on e-scooters and keep people safe?”