Children were heading back from a picnic when their driver stopped to get a drink and their bus was hit by an airstrike, according to Save the Children.
Coalition airstrikes led by Saudi Arabia hit the bus carrying children in rebel-held northern Yemen on Thursday, killing and wounding dozens.
The bus had been travelling through a busy market in Dahyan district, northern Saada, at the time of the raid.
The Houthi rebels' health ministry said 43 people died, including 29 children.
"Scores killed, even more injured, most under the age of 10," Johannes Bruwer, head of delegation for the International Committee for the Red Cross (ICRC) in Yemen, stated in a Twitter post.
The ICRC said one of the hospitals it supports was treating the wounded.
In a video recorded in the immediate aftermath of the attack, one boy covered in dirt trying to stand up was seemingly unable to move.
"My leg won't get up," he told the man behind the camera.
Mohammed Abdul-Salam, a Houthi spokesman, accused the coalition of showing a "clear disregard for civilian life" by targeting a crowded public place.
Footage from the hospital showed young children, some still wearing their backpacks, bleeding and apparently injured.
"It is high time for these relapsing tragedies to stop in Yemen," said Robert Mardini, the ICRC's regional director.
"No one should allow putting children in harm's way and making them pay such an unacceptable price."
The Houthi rebels control much of northern Yemen, including the capital, Sanaa.
The Dahyan district hit on Thursday lies close to the Saudi border. In recent months, rebels have fired missiles into the neighbouring kingdom, including on Wednesday in an attack that killed one.
Col Turki al-Malki, a spokesman for the Saudi-led coalition, said the attack in Saada targeted the rebels who had fired it.
He said it was carried out "in accordance with international and humanitarian law and customs", and accused the rebels of using the children as human shields.
The coalition intervened in 2015 to try to restore the internationally recognised government to power after it was driven out of Sanaa by Shia rebels.
The coalition, which receives support and funding from the US and UK, has been criticised for its often indiscriminate bombing of civilian areas.