At 5.10pm, an 18-year-old man riding a grey Piaggio moped was travelling west on a narrow section of Blackfriars Road, at the junction with Hyde Park Road.
A vehicle, described as a black 4×4, travelling in the opposite direction then collided with him before driving away from the scene.
The moped driver was left with an injured ankle.
The driver of the 4×4 is reported to be a woman with blonde hair.
PC Nick Gard said: “We are appealing for witnesses to identify the 4×4 vehicle and its driver.
“Did you see what happened, or have CCTV or dashcam footage showing the incident?
“If you were the driver, we are keen to speak to you to find out what happened, so please get in touch with us.”
If you have any information about this incident, call us on 101 quoting reference number 44210163694.