The coalition entered Yemen's civil war more than three years ago to fight northern Houthi rebels who seized power away from Yemen's internationally recognized government.
It accused the Houthis of using children as human shields and said the strikes were carried out in accordance with worldwide humanitarian law.
"We are unable to verify the details at this moment", Save the Children wrote on August 9.
Last week, Yemeni medical officials said the coalition conducted airstrikes in the rebel-held port city of Hodeida, killing at least 28 people and wounding 70.
The International Committee of the Red Cross (ICRC) said a hospital it supported in Saada had received dozens of casualties after the attack.
The missile was sacked from Amran province in northern Yemen on Wednesday night, the coalition said in a statement published by the Saudi Press Agency.
The coalition fighting alongside the government against Shiite Huthi rebels in Yemen said it carried out a "legitimate military action" in the area.
The coalition has insisted it never deliberately targets civilians but human rights groups have accused it of bombing markets, schools, hospitals and residential areas.
"Grotesque, shameful, indignant. Blatant disregard for rules of war when bus carrying innocent school children is fair game for attack", Jan Egeland, head of the Norwegian Refugee Council, said in a Twitter post. "This is why we need an independent investigation into attacks on civilians so that perpetrators can be held to account", Ghaly added.
Al-Malki insisted Thursday's attack carried out in Saada is a "legitimate military action" and is 'in accordance with global humanitarian law and customs.' He also accused the Houthis of recruiting children and using them in the battlefields to cover for their actions.
"(The air strikes) conformed to global and humanitarian laws", the coalition statement said, quoting spokesman Colonel Turki al-Malki.
"We trust when they say that they will investigate that they will investigate". The simultaneous power vacuum and crippling of Yemen's already-weak health and security infrastructures have enabled al Qaeda and ISIS affiliates to operate, albeit under threat of USA airstrike, and unleashed a tsunami of starvation and disease.
Worldwide rights groups repeated calls for an end to the war and strongly condemned the bus attack and other civilian massacres.
The Houthis have fired dozens of missiles into the kingdom in recent months, part of a three-year-old conflict widely seen as a proxy battle between regional rivals Saudi Arabia and Iran.
He said the leaders and militants responsible for launching ballistic missiles and targeting civilians would be held accountable as part of the coalition's efforts to prevent terrorist elements from compromising regional and worldwide security.
The war in the impoverished country has since left almost 10,000 people dead and unleashed what the United Nations describes as the world's worst humanitarian crisis.