In a statement Thursday, the Saudi-led coalition said the strike was a "legitimate military action to target elements that planned and carried out" an attack that targeted civilians in Jizan, a border city in southwest Saudi Arabia.
The International Red Cross says the airstrike hit a bus full of children, parked in a busy market in Dahyan, in Sa'ada province - controlled by the Houthis.
CNN reported that dozens of children under the age of 15 were killed in the attack, and many more were injured, according to reports from Yemeni officials and the Red Cross. He said this made the attack a "legitimate military action in accordance with global humanitarian law".
Al-Masirah, the TV station of the armed Houthi movement, said on its Twitter account that 39 people had been killed and 51 wounded.
The Iranian backed Houthi rebels seized the capital of Sanaa in 2014 and overthrew the internationally recognised government led by President Abdrabu Mansur Hadi during a transition of power from former president Ali Abdullah Saleh.
"Shrapnel from the intercepted missile scattered over residential areas, leaving a Yemeni resident killed and 11 other civilians wounded", the coalition said.
Maliki said those responsible for firing ballistic missiles and targeting civilians would "get what they deserve".
Col al Maliki said that the coalition targeted the Houthi militia members who were inside the bus and said that they were the planners and operators of the missiles launch pads.
The United States is helping the coalition, the only party in the conflict to use war planes, with refueling, intelligence, and billions in weapons sales. The coalition denied that it had carried out air strikes in the area, and blamed the deaths on rebel mortar fire.
Aid agency CARE International noted that Thursday's strike came a week after the Hodeida bombardment.
Thursday's attack marks a grim milestone in a war that lately has seen yet another escalation, as coalition-backed Yemeni government forces have made a recent push to reclaim the key port city of Hodeidah from rebels.
"We call on the Saudi-led coalition to conduct a thorough and transparent investigation into the incident", she said.
In a statement released through the state-run Saudi Press Agency, Riyadh called the airstrike a "legitimate military action" conducted in accordance with worldwide law.
The Houthis have launched a series of missile strikes on the kingdom, including the capital, Riyadh, over the past year. There was no immediate comment from the Houthis in response to the coalition allegations.
Impoverished Yemen, on the southern tip of the Arabian Peninsula, is now in the world's worst humanitarian crisis, with more than 22.2 million people in need of assistance.
The U.N. special envoy for Yemen, Martin Griffiths, has been pushing to bring the warring parties to restart peace talks.