The nine-year-old was walking with friends when it is believed he stepped into the path of a red motorbike on Sunday at about 1740 GMT.
The boy was thrown to the ground in the collision on Captain's Road.
The motorcyclist then failed to wait for police to arrive and left the scene. It is believed he turned onto Southhouse Terrace.
The boy suffered minor grazing to his right hip and elbow and was taken to the Royal Hospital for Sick Children in Edinburgh.
The motorcyclist is white, male, about 5ft 10in, 30-35 years old with a stubbly complexion.
He was wearing a motorcycle helmet, black leather jacket and either jeans or tracksuit bottoms.
A Lothian and Borders Police spokesman said: "Leaving the scene of a road collision without speaking to the police is serious and we would appeal to this gentleman to contact us immediately.
who can help us trace his whereabouts or has information that can
assist with our investigation should also get in touch."
Source: BBC News
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