"Last year was one of the worst in recent memory for children in countries affected by conflict," the UN leader said, adding he is "deeply alarmed at the suffering of so many children as a result of Israeli military operations in Gaza last year."
More than 500 children died during the conflict in Gaza last year. A United Nations report accused the Israeli army of being responsible for strikes on buildings where civilians were sheltering during the conflict.
"I urge Israel to take concrete and immediate steps, including by reviewing existing policies and practices, to protect and prevent the killing and maiming of children, and to respect the special protections afforded to schools and hospitals," the UN leader said.
Despite the admonitions for Ban, the United Nations has not included Israel on a list of countries singled out for violating the rights of children.
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Last year's war killed 2,200 Palestinians, mostly civilians, and 73 on the Israeli side, 67 of them soldiers.
The international community has called for an end to Israel's blockade of Gaza, now in its ninth year, which puts tight restrictions on the entry of building material through the goods crossing the Jewish state controls.
Israel however says it fears building materials could be used by Hamas to build weapons and attack tunnels.