"This one millionth child refugee is not just another number. This is a real child ripped from home, maybe even from a family, facing horrors we can only begin to comprehend," said the head of UN children's agency UNICEF, Anthony Lake, said in a statement.
Children make up half of all refugees from more than two years of conflict in Syria, according to United Nations figures.
Most Syrian refugees have found a haven in Lebanon, Jordan, Turkey, Iraq and Egypt, but they are increasingly fleeing to North Africa and Europe.
"What is at stake is nothing less than the survival and wellbeing of a generation of innocents," Antonio Guterres, the UN high commissioner for refugees.
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"The youth of Syria are losing their homes, their family members and their futures. Even after they have crossed a border to safety, they are traumatised, depressed and in need of a reason for hope," he added.
Inside Syria, meanwhile, more than two million children have been driven from their homes in the face of the conflict, which has morphed into a vicious, sectarian civil war.
According to the UN's human rights division, some 7,000 of the dead were youngsters.
The UN also warned that refugee kids face the threat of child labour, early marriage and the potential for sexual exploitation and trafficking.
More than 3,500 children in Jordan, Lebanon and Iraq have crossed Syria's borders either unaccompanied or separated from their families, it added.
Aid agencies have scrambled to meet the needs of refugee children, for example by vaccinating hundreds of thousands against measles and providing schools in camps.