There was no immediate comment from the coalition, which intervened in 2015 to try to restore the internationally recognized government to power after it was driven out of the capital Sanaa by the rebels.
"Shrapnel from the intercepted missile scattered over residential areas, leaving a Yemeni resident killed and 11 other civilians wounded", the coalition said.
It accused the Saudi-led coalition fighting the Shiite rebels on the side of the government of hitting the bus in an air strike.
Fragments from the Houthi missile launched at Jizan Industrial City had killed one Yemeni civilian and wounded 11, Saudi state media said earlier on Thursday.More news: Blues Set to Break World Record for Courtois Replacement
Yemeni tribal elders told the Associated Press that the bus was hit as it passed through the Dahyan market and that it was transporting local civilians, including many school children.
"Today's attack in Saada was a legitimate military operation. and was carried out in accordance with worldwide humanitarian law", the coalition said in the Arabic-language statement carried by SPA. "[ICRC] sending additional supplies to hospitals to cope with the influx".
The military alliance says it does not target civilians and has set up an investigation committee into alleged mass casualty air strikes which have mostly cleared the coalition of any blame.
It accused the Houthis of using children as human shields.More news: Premier League CEO reveals his dislike for Man City's dominance
The bus came under attack at a market in the Sa'ada town of Zahyn on Thursday, Yemen's al-Masirah television network reported. The coalition denied that it had carried out air strikes in the area, and blamed the deaths on rebel mortar fire.
Nearly 10,000 people - two-thirds of them civilians - have been killed and 55,000 others injured in the fighting, according to the United Nations.
The war in 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.More news: Tottenham make £25m bid to sign 22-year-old