There was no breakdown in the casualties and it was not immediately clear how numerous victims were on the bus itself and how many were pedestrians in the immediate area around it.
The spokesman of the coalition backing the legitimate Yemeni national army said that "the targeting that took place today in the governorate of Saada, is a legitimate military action to target elements that planned and carried out attacks targeting civilians yesterday evening in Jizan that killed and wounded civilians".
Nearly 10,000 people - two-thirds of them civilians - have been killed since the Houthi movement took control of much of the north of the country, including the capital Sanaa, in 2014, forcing President Abdrabbuh Mansour Hadi into exile in neighbouring Saudi Arabia.
In July, a Badr 1 missile was sacked at Jizan Economic City, where Saudi Aramco is building a 400,000-barrel-per-day refinery.
The coalition intervened in the conflict back in 2015 in an attempt to restore the internationally recognised government to power after it was driven out by rebels in the capital.
The alleged attack left one Yemeni resident dead and 11 civilians wounded, said Maliki.
The ballistic missile was sacked from the northern Yemeni province of Amran towards the southern Saudi city of Jizan, said a coalition statement published by the official Saudi Press Agency.
Al Masirah TV gave a different casualty toll, saying 39 people were killed and 51 wounded, mainly children.
Al-Malki insisted Thursday's attack in Saada was carried out "in accordance with worldwide and humanitarian law and customs".
Later on Thursday, airstrikes hit the Yemeni capital, Sanaa, and sounds of the blasts reverberated across the city's southern and western neighborhoods.
The Iran-backed Houthis have in recent months ramped up missile attacks against Saudi Arabia, which Riyadh usually says it intercepts. Its last air strike in Yemen was July 24 against Al Qaeda in the Arabian Peninsula, she said, adding that the command seeks to help partners mitigate civilian casualties.
Yemen's stalemated, three-year war has killed over 10,000 people, badly damaged Yemen's infrastructure and crippled its health system.
Yemen has been devastated by a conflict that escalated in early 2015, when the Houthis seized control of much of the west of the country and forced President Abdrabbuh Mansour Hadi to flee overseas.
A US military spokeswoman said: "U.S". But the coalition denied carrying out any attacks in the city, saying it follows a "strict and transparent approach based on the rules global law".
The Yemen war has killed more than 10,000 people, displaced more than 2 million and driven the country to the verge of starvation, according to the United Nations. We urge all parties to agree to an immediate cessation of hostilities, return to the negotiation table to commit to a ceasefire and cooperate with the UN Special Envoy Martin Griffiths. He recently announced plans to invite Yemen's warring parties to Geneva on September 6 to hold the first round of consultations.