"Today's attack in Saada was a legitimate military operation. and was carried out in accordance with global humanitarian law", the Arabic-language coalition statement said, quoting spokesman Colonel Turki al-Malki.
The International Committee of the Red Cross, citing local officials, announced that a total of 50 people have died in the attack and 77 have been injured, a lot of them children.
"Scores killed, even more injured, most under the age of 10", Johannes Bruwer, head of delegation for the ICRC in Yemen, said in a further Twitter post.
State news agency SPA later said one Yemeni resident in Jizan was killed.
"We call on the Saudi-led coalition to conduct a thorough and transparent investigation into the incident", she said.
"We see violations across the country and it's really sad to speak about civilian casualties in a matter of less than a week".
The bus had been travelling through a busy market in Dahyan district, northern Saada, at the time of the raid, which Houthi rebels' Al Masirah TV reported killed 39 and wounded 51, "mostly children".
The attack was also denounced by the United Nations children agency, UNICEF.
Most of the children were inside the bus when the airstrike hit, according to a local medic, Yahya al-Hadi.
Injured children, bloodied, bandaged and screaming, lay on stretchers as doctors treated them, friends and relatives having carried some of them in their arms to be treated.
Most of the images of the children hit by this airstrike are so gruesome the broadcasting rules don't allow us to show them - but a warning, the report still contains distressing images.
Saudi Arabia and some of its allies have been fighting in Yemen for more than three years against the Houthis, a rebel group who control much of north Yemen, including the capital Sanaa, and drove a Riyadh-backed government into exile in 2014.
The attack on Jazan was the second ballistic missile fired at Saudi Arabia by the Iran-backed rebels this week. "The attack today was a follow-up process to neutralise that threat".
"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.
Upon interception, Saudis say the missile exploded into fragments that killed one Yemeni civilian and injured 11 other people.
The missile was sacked from the rebel-held Yemeni province of Amran towards Jizan, the coalition said.
Wednesday's attack brings the tally to 165 rebel missiles launched since 2015, according to the coalition, which that year joined the Yemeni government's fight against Huthi rebels.
He stressed that the Houthi leaders and terrorist elements responsible for firing ballistic missiles and targeting civilians will be targeted as part of the coalition efforts to prevent terrorist elements from harming regional and global security.
Worldwide aid agencies denounced the attack and the loss of civilian lives.
"This latest air strike, only a week after the attacks on Hodeida city, demonstrates a continued disregard for human life and suffering", said Johan Mooij, the agency's country director in Yemen.
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.
Col. Al-Maliki stressed: "The Joint Forces Command of the Coalition will take all deterrent measures against such barbaric, frivolous launches in conformity with the worldwide humanitarian law, and those who support these terrorist crimes will be held accountable for their actions".