An additional one million children were born as refugees since the conflict erupted on March 15, 2011, UNICEF said.
"The war in Syria marks yet another shameful milestone today," said UNICEF executive director Henrietta Fore, who was in Syria last week.
"As the conflict enters its 10th year, millions of children are entering their second decade of life surrounded by war, violence, death and displacement."
Citing data from 2014 when official monitoring began, UNICEF said that "more than 9,000 were killed or injured in the conflict".
During the same time "close to 5,000 children - some as young as seven - were recruited into the fighting (and) nearly 1,000 education and medical facilities came under attack".
The agency warned that the "true impact of this war on children is likely to be more profound".
Ted Chaiban, UNICEF regional director for the Middle East and North Africa, said an ongoing offensive by government forces on the last rebel stronghold in northwestern Syria was having "severe consequences on children".
Fighting there since December 1 has displaced more than 960,000 people, including over 575,000 children, according to UNICEF.
And as a result of the wider impact of the conflict "more than 2.8 million children are out of school inside Syria and in neighbouring countries," the agency said.
Two in five schools cannot be used because they are destroyed, damaged, sheltering displaced families or being used for military purposes, said UNICEF.
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Addressing warring parties, Fore said: "Our message is clear: Stop hitting schools and hospitals.
"Stop killing and maiming children. Grant us the crossline and cross-border access we need to reach those in need. Far too many children have suffered for far too long."