Teachers have accused the club of "emotional blackmail" and say they should have been consulted about the move.
Jock Brown, Celtic's chief executive, and Eric Black, the development manager, informed schools that boys who join Celtic "will no longer be available to play schools football" to reduce the "many demands at a significant time in their personal, physical and educational development".
Eventually boys of all ages will be excluded. The club said the aim was that young players would take part in no more than 30 competitive matches a season.
Harry Paton, president of Glasgow Schools' Football Association and principal teacher of physical education at St Margaret Mary's Secondary, said: "This is blatant commercial exploitation and detrimental to the development of these young boys.
"All that Celtic plc are interested in is getting a cheap product and they are indulging in a form of emotional blackmail by imposing this pressure on young players and their parents."
Mr Paton said that young players did not play full competitive matches since the association complied with the Scottish Football Association guidelines on seven-a-side games.
Bruce Malone, headteacher of St Andrew's Secondary, Glasgow, said there was "genuine concern" and insisted: "Schools football should come first."
Jim Sinclair, the Scottish Football Association's youth director, said other clubs might follow Celtic's lead. The SFA has called a meeting to thrash out a stance on schools football with Premier League clubs and others.
Mr Black told The TESScotland: "This system which is practised on the continent and in England has the aim of limiting the number of competitive matches which the player is involved in and focusing on a structured coaching programme. Skill development is the overriding principle of development at Celtic."