The drone strike on the town of Al Deir, in Hajjah governorate, on Monday killed Yousef Abdoh Bishi and seriously injured three others, Yemeni Information Minister Moammar Al Eryani said.
“We condemn the terrorist Houthi militia's criminal attack on Al Salam school in the town of Al Deir in Hajjah governorate during school hours, using an Iranian-made drone,” Mr Al Eryani wrote on Twitter.
“The Houthi targeting of a school that is not inside an area of military confrontation could have caused hundreds of innocent children to fall victim.
“This once again confirms the Houthi's undermining of efforts for de-escalation and its insistence on a path towards escalation, without caring for the blood and souls of Yemenis.”
A UN-brokered truce between the warring sides that had lasted six months was not renewed in October.
The Houthi rebels had insisted on new regulations regarding fuel imports, which the government said do not comply with international law.
Since then, 62 children have been killed in the conflict, the UN children’s fund has said.
The Houthis have also launched several attacks on commercial tankers in recent weeks, describing the moves as “warnings”.
On Monday, Unicef said at least 11,000 children in Yemen have been killed or injured during the eight-year war — an average of four children a day since 2015.
“Thousands of children have lost their lives and hundreds of thousands more remain at risk of death from preventable disease or starvation,” it said.
The UN, US, EU and Gulf states have continued to work on reviving the truce, which began on April 2.
“We must preserve the positive momentum and gains made since April,” US special envoy to Yemen Tim Lenderking said earlier this month.
Despite the breakdown of talks, Mr Lenderking said engagement among warring parties has intensified.
Houthi rebels took the capital Sanaa in 2014. A Saudi-led alliance intervened at the request of the Yemen's internationally recognised government the following year.