The kids were travelling on a bus that was hit at a market in Dahyan, in the northern province of Saada.
According to the health ministry run by the rebel Houthi movement, the death toll at 43. It said 61 people were wounded.
The coalition, which is backing Yemen’s government in a war with the Houthis, said its actions were “legitimate”.
It insists it never deliberately targets civilians, but human rights groups have accused it of bombing markets, schools, hospitals and residential areas.
Yemeni tribal elders told the AP that the bus was hit as it passed through Dahyan market and that it was transporting local civilians, including many school children.
Save the Children said it had been told by its staff that the kids were on their way back to school from a picnic when the driver of their bus stopped to get a drink.
The bus was stationary when the attack happened, it added.
The ICRC said a hospital it supported in Saada had received the bodies of 29 children, all of them under the age of 15, and 48 injured people, among them 30 children.
It sent additional supplies to the hospital to cope with the influx of patients.
Houthi-run Al-Masirah TV reported that 47 people were killed and 77 wounded, and broadcast pictures showing the bodies of several young children, some of them wearing school uniform.
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