"Shrapnel from the intercepted missile scattered over residential areas, leaving a Yemeni resident killed and 11 other civilians wounded", the coalition said.
The US State Department called on Thursday for the Saudi-led coalition to investigate the air strikes.
Earlier, Maliki accused the Houthis of "recruiting child soldiers, throwing them in battlefields and using them as tools".
The assault was the latest in a string of airstrikes to target civilians by an American-backed regional coalition led by Saudi Arabia and the United Arab Emirates.
Footage provided by the rebels' Ansarullah Media Centre showed a number of wounded children lying two to a hospital bed, while in a separate shot medics tend to casualties in a crowded room.
The world has forgotten Yemen's bloody war, but when you look at these young victims - their tiny bodies, some still struggling for life - you won't be able to forget them.
The head of the humanitarian organisation's delegation in the country, Johannes Bruwer, later tweeted that "scores" had been killed and "even more injured, most under the age of 10".
At least 43 people were killed and 63 injured in the strike, according to the Houthi-held health ministry.
The children were traveling on a school bus that was hit by a Saudi coalition airstrike in Dahyan, the BBC reported.
A Saudi Arabian blockade has contributed to starvation and disease while a United Nations report found the Saudi-led bombing campaign - carried out with USA support - has hit schools, even weddings.
"The Secretary-General calls on all parties to respect their obligations under worldwide humanitarian law, in particular the fundamental rules of distinction, proportionality and precautions in attack", his spokesperson, Farhan Haq, said Thursday.
On August 2, attacks on a hospital and a fish market in the strategic rebel-held port city of Hodeida killed at least 55 civilians and wounded 170, according to the ICRC.
The Iran-aligned Houthis regularly fire into Saudi Arabia and have targeted its capital, Riyadh, with ballistic missiles.
The Saudi-led coalition waging war on Yemen remained brazenly defiant on its new crime, calling the massacre a "legitimate action".
According to Al Jazeera, the Saudi coalition claimed it had targeted "missile launchers", but Yemen-based reporters who have witnessed numerous attacks in civilian-populated areas vigorously disputed the claim.
It is with the stated aim of dislodging the Houthis, and restoring the previous government, that the Sunni coalition has waged a years-long airstrike campaign in the country with the support of the U.S. Since large-scale fighting erupted in 2015, the ensuing violence has left more than 10,000 people killed and the country's health infrastructure so badly battered, almost 18 million Yemenis lack reliable access to food.
In another video, which appears to show the immediate aftermath of the strike, several lifeless bodies of children lay under a blown-up bus.
Global rights groups repeated calls for an end to the war and strongly condemned the bus attack and other civilian massacres. "Parties to the conflict and those who have influence over them, including Security Council members, can and should choose to end this catastrophe for the sake of Yemen's children".