Fragments from a missile launched into Saudi Arabia from Yemen by Houthi forces killed one civilian and wounded 11, Saudi state media said on Thursday.
The coalition has insisted it never deliberately targets civilians but human rights groups have accused it of bombing markets, schools, hospitals and residential areas.
Saudi Arabia, the United Arab Emirates and their allies intervened in the conflict the following March, aiming to push back the Houthis and restore the internationally recognised government to power.
"Today's attack in Saada was a legitimate military operation... it conformed to global and humanitarian laws", said coalition spokesman Colonel Turki al-Malki in the statement.
"Scores killed, even more injured, most under the age of 10", Johannes Bruwer, head of delegation for the International Committee for the Red Cross (ICRC) in Yemen, said in a twitter post.
He said additional supplies were being sent to hospitals to cope with the influx.
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The bus had been travelling through a busy market in Dahyan district, northern Saada, at the time of the raid, which Houthi rebels' Al Masirah TV reported killed 39 and wounded 51, "mostly children".
The Western-backed alliance fighting the Iranian-aligned Houthi group in Yemen said the air strikes targeted missile launchers used to attack the southern Saudi industrial city of Jizan, killing a Yemeni civilian there, a statement carried by the state news agency SPA said.
He accused the rebels of using children as "tools and covers for their terrorist acts".
Children have been killed or wounded in an attack on a bus in northern Yemen, the International Committee of the Red Cross says. The coalition denied that it had carried out air strikes in the area, and blamed the deaths on rebel mortar fire.
Yemen's war has left almost 10,000 people dead since 2015 and unleashed what the United Nations describes as the world's worst humanitarian crisis.