It happened in Aitnamona Crescent at 20:50 GMT on Sunday.
He was taken to hospital for treatment to his injuries which are not thought to be life threatening.
Ch Insp Norman Hanslet said: "To shoot anyone is bad enough but this is blatant child abuse and there should be no place for the shooting of a child in today's society."
"I know that the local community abhor this type of behaviour and I would ask people to support and assist police to bring these people to justice."
Police appealed for anyone with information to contact them.
A 16-year-old has been shot in both legs in a paramilitary-style attack in west Belfast.