The western-backed coalition fighting the rebel Houthi group in Yemen said the air strikes on Thursday targeted missile launchers used to attack the southern Saudi industrial city of Jizan, which killed a Yemeni civilian there, according to the state news agency SPA.
That was the toll at just one hospital.
A doctor treats children injured by the airstrike.
A military coalition led by Saudi Arabia and the United Arab Emirates got involved in Yemen's civil war in 2015.
"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.
"Scores killed, even more injured, most under the age of 10", Johannes Bruwer, head of delegation for the ICRC in Yemen, said in a further Twitter post.
Unicef, the United Nations children's agency, said on Twitter that there were "no more excuses...."
UNICEF Regional Director in the Middle East and North Africa Geert Cappelaere also responded to Thursday's strike, asking, "Does the world really need more innocent children's lives to stop the cruel war on children in Yemen?"
Yemen's stalemated, three-year war has killed over 10,000 people, badly damaged Yemen's infrastructure and crippled its health system.
"We are certainly concerned about the reports that there was an attack that resulted in the deaths of civilians".
"The place is known to be a market, [and] there is no military installation nearby. but the Saudis are known to have done this many times-target schools, weddings and so on", Nasser Arrabyee told Al Jazeera.
Coalition spokesman Turki al-Maliki told AFP that claims by aid organisations that children were inside the bus were "misleading", adding that the bus carried "Huthi combatants". Say: I want the State Dept to condemn the Saudis for bombing Yemeni children and I want the U.S. to stop selling weapons to Saudi Arabia. "We closely coordinate with them", spokeswoman Heather Nauert said.
ICRC said one of the hospitals it supports was treating the wounded.
Col. Al-Maliki reported that the ballistic missile was launched deliberately by the terrorist Iranian Houthi militias to target densely-populated civilian areas in Jazan, Saudi Arabia, where the missile was intercepted and destroyed by the Royal Saudi Air Defense.
The Saudi government issued a statement on August 9 and described the strike as "a legitimate military action" and was "conducted in conformity with the worldwide humanitarian law".
Col. Al-Maliki stressed: "The Joint Forces Command of the Coalition will take all deterrent measures against such barbaric, frivolous launches in conformity with the global humanitarian law, and those who support these terrorist crimes will be held accountable for their actions".
Saada, the main stronghold of the Houthis, has mainly come under air strikes from the coalition as the mountainous province makes battles hard for pro-government ground troops.
So far, almost 10,000 people have died in the war in Yemen, which has unleashed what the United Nations describes as the world's worst humanitarian crisis.