The children were on a summer school field trip when their bus was struck at a market, the first stop of the day, killing 50 and injuring 77.
Images broadcast by Houthi media showed scores of bloody children, some still wearing their backpacks as they were loaded onto stretchers.
"Targeting Saudis and residents in Saudi is a red line", coalition spokesman Turki al-Malki later told Al Arabiya TV.
The UN children's agency UNICEF said it was "very concerned with the initial reports of children being killed". The fact that this was a high profile attack scattering the bodies of children across a crowded market is only going to make things worse.
However, a recent review of airstrikes by the United Nations found that "measures taken by the Saudi Arabia-led coalition in its targeting process to minimize child casualties, if any, remain largely ineffective".
"Putting children in harm's way is horrific and deplorable and making them pay such a price is unacceptable", she said.
The coalition said the strike targeted the Iran-backed Huthi rebels responsible for a deadly missile attack on the Saudi city of Jizan on Wednesday.
On Wednesday night, Col. Al-Maliki stated that at (20:34) the Coalition Air Defense detected a ballistic missile launch from Northern Amran in Yemen, aimed at Saudi Arabia.
They say their missile attacks on the kingdom are in retaliation for air raids on Yemen by the Western-backed coalition.
The Houthis seized the capital, Sanaa, in 2014 and overthrew the internationally recognised government led by President Abdrabu Mansur Hadi during a transition of power from former president Ali Abdullah Saleh. It also said the missile was launched "deliberately to target residential and populated areas".
It accused the Houthis of using children as human shields and said the strikes were carried out in accordance with worldwide humanitarian law. "Central Command was not involved in the air strike in Saada".
The missile was sacked from the rebel-held Yemeni province of Amran towards Jizan, the coalition said.
"The Secretary-General calls on all parties to respect their obligations under worldwide humanitarian law, in particular the fundamental rules of distinction, proportionality and precautions in attack", his spokesperson, Farhan Haq, said Thursday.
The coalition denied responsibility for those attacks.
"This latest air strike, only a week after the attacks on Hodeida city, demonstrates a continued disregard for human life and suffering", said Johan Mooij, the agency's country director in Yemen.
The Yemen war has killed more than 10,000 people, displaced more than 2 million and driven the country to the verge of starvation, according to the United Nations.
The United States is helping the coalition, the only party in the conflict to use war planes, with refueling, intelligence, and billions in weapons sales.