The International Committee of the Red Cross (ICRC) said a hospital it supported in Saada had received dozens of casualties on Thursday after the attack.
But the International Committee of the Red Cross said the strike hit a bus filled with children in the Huthi stronghold of Saada, causing dozens of casualties.
One person was killed in that attack, Saudi state media reported. The province lies along the border with Saudi Arabia.
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.
According to the United Nations human rights office, more than 16,000 civilians have been killed or injured since the war began, the vast majority by airstrikes.
Worldwide aid groups were quick to condemn the air strike.
"This is yet another example of the blatant violations of worldwide humanitarian law that we have seen in Yemen over the past three years-from indiscriminate and disproportionate attacks on civilians, denial of access to humanitarian aid and the use of starvation as a weapon of war-it's the people of Yemen, not the warring parties, who are paying the ultimate price".
Upon interception, Saudis say the missile exploded into fragments that killed one Yemeni civilian and injured 11 other people.
Yemeni tribal leaders told the AP the Saudi-led USA -backed coalition fighting Shiite Houthi rebels was behind the airstrike.
Maliki said those responsible for firing ballistic missiles and targeting civilians would "get what they deserve".
The Iran-aligned Houthis regularly fire into Saudi Arabia and have targeted its capital, Riyadh, with ballistic missiles.
Colonel Turki al-Malki, a spokesman for the Saudi-led coalition, said the missile strike was aimed at a "legitimate target".
The coalition said Wednesday's attack brought the tally of rebel missiles launched since 2015, the year it joined the Yemeni government's fight against the rebels, to 165.
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".
The first day of the campaign rounded up 500 weapons from tribal members in the area, said Col Al Buhar.
Saudi Arabia, the driving force behind a coalition of its Arab neighbors, saw no reason to apologize, however.
"It's hard to believe we live in a world where children should live in fear of such attacks, yet here we are", she added.
So far, almost 10,000 people have died in the war in Yemen, which has unleashed what the United Nations describes as the world's worst humanitarian crisis.
Earlier this week, the UN Special Envoy for Yemen, Martin Griffiths, convened a consultative meeting in the United Kingdom of 22 Yemeni public figures and women activists as part of his efforts to end the war.