There was no immediate comment from the coalition, which is led by Saudi Arabia and which is fighting to restore Yemen's internationally recognized government to power.
A Saudi Arabian blockade has contributed to starvation and disease while a United Nations report found the Saudi-led bombing campaign - carried out with US support - has hit schools, even weddings.
"This is yet another example of the blatant violations of worldwide humanitarian law that we have seen in Yemen over the past three years-from indiscriminate and disproportionate attacks on civilians, denial of access to humanitarian aid and the use of starvation as a weapon of war-it's the people of Yemen, not the warring parties, who are paying the ultimate price", said Sylvia Ghaly, director of advocacy in Yemen for Save the Children.
"A total of 43 people, mostly pupils under the age of 10, were killed and 64 were injured when two Saudi-led airstrikes hit passenger buses in Dahyan popular market", Yahya Shayem, head of Saada Health Office, told Xinhua news agency.
Saudi Arabia shot down a missile fired by the Huthis on Wednesday, with debris killing a Yemeni man and wounding 11 others, the coalition said.
"The coalition will take all necessary measures against the terrorist, criminal acts of the terrorist Iranian-Houthi militia, such as recruiting child soldiers, throwing them in battlefields and using them as tools and covers to their terrorist acts", Col Al Malki 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.
The missile was sacked from the rebel-held Yemeni province of Amran towards Jizan, the coalition said.
Global aid groups were quick to condemn the air strike.
It was not immediately clear whether the bus was the target of the air strike, but coalition spokesman Col Turki al-Malki said the attack was "a legitimate military action, conducted in conformity with worldwide humanitarian law".
Global rights groups repeated calls for an end to the war and strongly condemned the bus attack and other civilian massacres.
Thursday's attack marks a grim milestone in a war that lately has seen yet another escalation, as coalition-backed Yemeni government forces have made a recent push to reclaim the key port city of Hodeidah from rebels. The coalition denied that it had carried out air strikes in the area, and blamed the deaths on rebel mortar fire.
Saudi Arabia, the UAE and their allies in the Arab Coalition intervened in the conflict at the request of Mr Hadi's government.
"It's hard to believe we live in a world where children should live in fear of such attacks, yet here we are", she added.
There was a horrifying attack Thursday in Yemen - a Middle Eastern country torn apart by a 3-year-old civil war.
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