Police are appealing for any witnesses and drivers with dashcam footage which may have caught the fatal incident in East Dulwich Grove at around 9.15pm.
The moped rider, a 22-year-old man, was travelling in the direction of Thorncombe Road when he hit the tree, police said.
His family have been informed of his death and the Metropolitan Police are yet to establish if any other vehicles were involved.
A Met spokesperson said: “Officers from the Serious Collision Investigation Unit are investigating.
“They are particularly keen to hear from any drivers who were in East Dulwich Grove from 9pm onwards and who may have recorded the events leading up to the collision on dashcam.
“Any witnesses yet to speak with police are asked to call the SCIU at Catford Traffic Garage on 020 8285 1574 quoting CAD 7891/19July.”