More than 60 people were wounded.
One missile struck a bus taking children back from a summer school picnic.
Television pictures from a hospital showed blood-covered youngsters who seemed too stunned to even cry. Others writhed on the floor, waiting for help.
"Grotesque, shameful, indignant," Norwegian Refugee Council head Jan Egeland tweeted. "Blatant disregard for rules of war when a bus carrying innocent schoolchildren is fair game for attack."
Save the Children said it "condemns this horrific attack and is calling for a full, immediate, and independent investigation into this and other recent attacks on civilians and civilian infrastructure."
Doctors Without Borders decried that "civilians continue to pay the highest price" in Yemen, while the regional director of the U.N. Children's Fund asked, "Does the world really need more innocent children's lives to stop the cruel war on children in Yemen?"
The United States backs the Saudi-led coalition targeting Iranian-supported Houthi rebels in Yemen.
"We trust when they say that they will investigate. We closely coordinate with them," State Department spokeswoman Heather Nauert said.
Response to Houthi strike
Thursday's airstrike was carried out against a rebel-held area in Saada province, near the Saudi border. Missiles struck a market.
Wounded children, bloodied, bandaged and screaming, laid on stretchers as doctors treated them, friends and relatives having carried them in their arms to be treated.
The International Committee of the Red Cross said on Twitter that its team at an ICRC-supported hospital in Saada received the bodies of 29 children, all under 15 years old.
It also received 48 wounded people, including 30 children, it said.
A spokesman for the Red Cross in Sanaa told AFP the toll was not final as casualties from the attack were taken to several hospitals.
The attack took place in the Dahyan market in Saada province, a Houthi stronghold.
The province lies along the border with Saudi Arabia.
The bus was ferrying children coming from summer school, according to the Saada health department and Yemeni tribal leaders.
"Our shops were open and shoppers were walking around as usual. All of those who died were residents, children and shop owners," witness Moussa Abdullah, who was being treated in hospital for wounds, told Reuters.
Saudi's called Thursday's airstrike "a legitimate military operation ... carried out in accordance with international humanitarian law."
Last week, attacks on a hospital and a fish market in the strategic rebel-held port city of Hudaida killed at least 55 civilians and wounded 170, according to the ICRC.
According to the UNICEF, since conflict escalated in 2015, about 2,500 children have been killed and 3,600 maimed in Yemen.
Popular forces seized the Yemeni capital of Sanaa during 2014 uprising, sending the Western-supported government into exile in Saudi Arabia.
The Saudi-led coalition, backed by United States began its air and ground campaign to retake Sanaa from rebels aligned to Iran more than three years ago. Its airstikes have obliterated civilian neighborhoods, including schools and hospitals, and compounded the misery of what is one of the world's worst humanitarian disasters.
Many Yemenis are near starvation. There are also severe shortages of fresh water and medicine. A cholera epidemic has killed thousands over the last two years. Johannes Bruwer, head of delegation for the ICRC in Yemen, also said in a tweet that most of the victims were under the age of 10.
Elsewhere, Saudi fighter jets pounded Zabid District in Yemen's western province of Hudaydah, killing two civilians and injuring one child.
Saudi Arabia and some of its allies, particularly the United Arab Emirates, launched a brutal war, code-named Operation Decisive Storm, against Yemen in March 2015 in an attempt to reinstall former Yemeni President Abd Rabbuh Mansur Hadi, a staunch ally of Riyadh, and crush the popular Ansarullah movement.
The offensive initially consisted of a bombing campaign, but was later coupled with a naval blockade and the deployment of ground forces into Yemen.
Thousands of Yemeni children in the city of Hudaydah are at risk of death, disease and starvation due to Saudi Arabia's ongoing military aggression, rights groups warn.
The imposed war has so far failed to achieve its goal, thanks to firm resistance mounted by Yemeni troops and Houthi fighters, but has unleashed the world's worst humanitarian crisis in the poorest Arabian Peninsula state.