23 August 2013 Last updated at 00:25 ET
The UN says about three quarters of the refugee children are under 11
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UN agencies say the number of children forced to flee Syria has reached one million, describing the figure as "a shameful milestone".
The UN's refugee agency and Unicef say a further two million children are displaced within the country.
It comes amid calls for an investigation into the latest claims of chemical weapons attacks in Syria.
More than 100,000 people have been killed in the conflict, according to UN Secretary General Ban Ki-moon.
'Traumatised'The UNHCR and Unicef say children now make up half of all refugees fleeing Syria. About three-quarters of those children are under 11.
"The youth of Syria are losing their homes, their family members and their futures," said UNHCR high commissioner Antonio Guterres.
"Even after they have crossed a border to safety, they are traumatised, depressed and in need of a reason for hope."
Most of the children have arrived in Lebanon, Jordan, Turkey, Iraq and Egypt, the UN says, and increasingly Syrians are fleeing to North Africa and Europe.
But with its appeal for Syria less than 40% funded, the two agencies say they are struggling to meet the needs of the refugees.
Just 118,000 of the refugee children have been able to continue in some sort of education, and a fifth have received psychosocial counselling.
Lebanon is one of the main countries hosting Syrian refugees
The BBC's Imogen Foulkes in Geneva says the agencies are now warning of a lost generation that are ill-equipped to bring peace and stability to their country in the future.
"We must all share the shame," said Unicef executive director Anthony Lake, "because while we work to alleviate the suffering of those affected by this crisis, the global community has failed in its responsibility to this child.
"We should stop and ask ourselves how, in all conscience, we can continue to fail the children of Syria."
Worst refugee crisisSyrian opposition activists say hundreds of people died when government forces launched chemical weapons attacks in the Ghouta area of the capital, Damascus, on Wednesday. Unverified footage showed civilians - many of them children - apparently suffering horrific symptoms, as well as rows of shrouded bodies.
The Syrian army deny the claims, saying they are part of a "filthy media war".
The UN has asked the Syrian government to let UN weapons inspectors already in the country to be allowed to investigate the latest reports.
The team currently only has a mandate to visit three previously agreed sites, including the northern town of Khan al-Assal, where some 26 people were killed in an alleged chemical attack in March.
But there is no sign as yet that Damascus will allow them to extend their mission.
The UN says the conflict in Syria has caused the world's worst refugee crisis for 20 years, with numbers not seen since the 1994 genocide in Rwanda.
It says more than 1.7million people have registered as refugees since the uprising against the rule of Syrian President Bashar al-Assad began in March 2011.
More than 40,000 Syrians have poured over the border of Iraqi Kurdistan since a new wave of arrivals began in the region a week ago.
Continue reading the main story
- Analysing film of attacks
- In pictures: 'Chemical attacks'
- City where snipers shoot children
- Kurdish-jihadist clashes
UN agencies say the number of children forced to flee Syria has reached one million, describing the figure as "a shameful milestone".
The UN's refugee agency and Unicef say a further two million children are displaced within the country.
It comes amid calls for an investigation into the latest claims of chemical weapons attacks in Syria.
More than 100,000 people have been killed in the conflict, according to UN Secretary General Ban Ki-moon.
'Traumatised'The UNHCR and Unicef say children now make up half of all refugees fleeing Syria. About three-quarters of those children are under 11.
"The youth of Syria are losing their homes, their family members and their futures," said UNHCR high commissioner Antonio Guterres.
"Even after they have crossed a border to safety, they are traumatised, depressed and in need of a reason for hope."
Most of the children have arrived in Lebanon, Jordan, Turkey, Iraq and Egypt, the UN says, and increasingly Syrians are fleeing to North Africa and Europe.
But with its appeal for Syria less than 40% funded, the two agencies say they are struggling to meet the needs of the refugees.
Just 118,000 of the refugee children have been able to continue in some sort of education, and a fifth have received psychosocial counselling.
The BBC's Imogen Foulkes in Geneva says the agencies are now warning of a lost generation that are ill-equipped to bring peace and stability to their country in the future.
"We must all share the shame," said Unicef executive director Anthony Lake, "because while we work to alleviate the suffering of those affected by this crisis, the global community has failed in its responsibility to this child.
"We should stop and ask ourselves how, in all conscience, we can continue to fail the children of Syria."
Worst refugee crisisSyrian opposition activists say hundreds of people died when government forces launched chemical weapons attacks in the Ghouta area of the capital, Damascus, on Wednesday. Unverified footage showed civilians - many of them children - apparently suffering horrific symptoms, as well as rows of shrouded bodies.
The Syrian army deny the claims, saying they are part of a "filthy media war".
The UN has asked the Syrian government to let UN weapons inspectors already in the country to be allowed to investigate the latest reports.
The team currently only has a mandate to visit three previously agreed sites, including the northern town of Khan al-Assal, where some 26 people were killed in an alleged chemical attack in March.
But there is no sign as yet that Damascus will allow them to extend their mission.
The UN says the conflict in Syria has caused the world's worst refugee crisis for 20 years, with numbers not seen since the 1994 genocide in Rwanda.
It says more than 1.7million people have registered as refugees since the uprising against the rule of Syrian President Bashar al-Assad began in March 2011.
More than 40,000 Syrians have poured over the border of Iraqi Kurdistan since a new wave of arrivals began in the region a week ago.