Al Masirah TV aired dramatic images of wounded children, their clothes and schoolbags covered with blood as they lay on hospital stretchers.
The bus was travelling through Dahyan market in Saada province at the time.
"The victims were the children in the bus, passersby and merchants in the market, and some injuries are serious, so the number of deaths may increase". It wasn't immediately clear how numerous casualties were on the bus and how many were pedestrians in the immediate area around it.
It said the air strike was aimed at missile launchers used to attack the southern Saudi city of Jizan on Wednesday, where a Yemeni civilian was killed. It also said the missile was launched "deliberately to target residential and populated areas".
"Under global humanitarian law, civilians must be protected during conflict", the ICRC said as alarm grew among worldwide aid agencies.
"The Coalition will take all necessary measures against the terrorist, criminal acts of the terrorist Iranian-Houthi militia, such as recruiting child soldiers, throwing them in battlefields and using them as tools and covers to their terrorist acts", coalition spokesperson Col.
But the International Committee of the Red Cross said the strike hit a bus filled with children in the Huthi stronghold of Saada, causing dozens of casualties.
US State Department spokeswoman Heather Nauert said the United States did not have the "full details of what happened on the ground" but said "we're concerned about these reports".
The United States has provided the Saudi-led coalition with weapons and logistical support during the three-year conflict. "This is why we need an independent investigation into attacks on civilians so that perpetrators can be held to account", Ghaly added.
"Scores killed, even more injured, most under the age of 10", Johannes Bruwer, head of delegation for the ICRC in Yemen, said in a Twitter post. It's not clear if there was any damage or casualties.
More than 10 thousand people have been killed as a result of the war in Yemen. That assistance has come under sharp criticism from Congress and the global community as civilian deaths have continued to multiply, even as the coalition promises not to target civilians.
The Saudi-led coalition is fighting to defeat Houthi rebels who expelled the Yemeni government from the capital and took control of vast swathes of the country.
"Our support to the coalition consists of aerial refueling and intelligence support to assist our partners in securing their borders from cross-border attacks from the Houthis".