The bus came under attack at a market in the Sa’ada town of Zahyn on Thursday, Yemen’s al-Masirah television network reported, according to presstv.ir.
The International Committee of the Red Cross (ICRC) said in a statement that the bus was carrying children.
Johannes Bruwer, head of delegation for the ICRC in Yemen, also said in a tweet that most of the victims were under the age of 10.
Elsewhere, Saudi fighter jets pounded Zabid District in Yemen’s western province of Hudaydah, killing two civilians and injuring one child.
Saudi Arabia and some of its allies, particularly the United Arab Emirates, launched a brutal war, code-named Operation Decisive Storm, against Yemen in March 2015 in an attempt to reinstall former Yemeni President Abd Rabbuh Mansur Hadi, a staunch ally of Riyadh, and crush the popular Ansarullah movement.
The offensive initially consisted of a bombing campaign, but was later coupled with a naval blockade and the deployment of ground forces into Yemen.
The imposed war has so far failed to achieve its goal, thanks to firm resistance mounted by Yemeni troops and Houthi fighters, but has unleashed the world's worst humanitarian crisis in the poorest Arabian Peninsula state.