The incident happened at about 15:45 in Allan Crescent in Dunfermline.
The 13-year-old boy was taken to Edinburgh Royal Infirmary, while a 12-year-old boy was treated at the scene by the Scottish Ambulance Service.
Police have appealed for anyone who may be able to help with their investigation to contact them on 101.
A 13-year-old boy is being treated in hospital for serious injuries after he and another boy were involved in collision with a bus in Fife.