The incident took place on Monday as the boy was crossing Saughton Road, close to the junction with Fairbrae at around 3.15pm on Monday.
A small black car was travelling northbound along Saughton Road when it collided with the boy, who was treated at hospital for minor injuries.
A spokesman for Police Scotland said: “Police in Edinburgh are investigating a hit and run collision in Saughton Road, north of the junction with Fairbrae, which took place around 3.15pm on Monday, January 29.
“The collision involved a small black car travelling towards Stenhouse Road and a pedestrian.
“An eight-year-old boy sustained minor injuries and attended the Sick Kids Hospital as a precaution.”