Two men were taken to hospital, and the 70-year-old pedestrian is currently in a critical condition.
Police added that the rider of the moped had been arrested at the scene.
The Met said in a statement officers were called around 11am on Friday after reports of a collision involving a pedestrian and moped on Maple Road in Penge.
The pedestrian, aged in his 70s, was taken to a south London hospital where he remains in a critical condition, police said, adding that his family have been informed.
The 24-year-old rider of the moped stopped at the scene, was arrested and taken to a south London police station, where he remains in custody.
Detectives from the Roads and Transport Policing Command are investigating and would like to speak with anyone who witnessed the incident or captured it on dash cam.
Those with relevant information are asked to call the Serious Collision Investigation Unit at Catford on 020 8285 1574.
A London Ambulance Service spokesperson said: “We were called at 10.57am today (16 April) to reports of a road traffic collision involving a motorcycle and a pedestrian on Maple Road, SE20.
“We sent two ambulance crews, an incident response officer, an emergency responder and a clinical team manager. We also dispatched London’s Air Ambulance.
“Two men were treated at the scene and taken to a major trauma centre as a priority.”