Syria's war is estimated to have killed nearly half a million people and displaced millions since it began with a brutal crackdown of anti-government protests in 2011. It escalated to pull in foreign powers and global jihadists.
"Children's needs, both inside Syria and in neighbouring countries, are growing," said Adele Khodr, UNICEF's Middle East chief.
"Many families struggle to make ends meet. Prices of basic supplies including food are skyrocketing, partially as a result of the crisis in Ukraine."
Children are among the most vulnerable and the UN warned they are bearing the brunt of the impact.
"In Syria's neighbouring countries, strained by political instability and fragility, nearly 5.8 million children depend on assistance, their lives riddled with poverty and hardship," Khodr added.
UNICEF said they faced a severe cash shortfall to provide aid.
"Funding for humanitarian operations is meanwhile fast dwindling," Khodr said. "UNICEF has received less than half of its funding requirements for this year."
UNICEF called for $20 million to fund "cross-border operations" in northwest Syria -- the country's last major rebel enclave -- to create "the only lifeline for nearly one million children".