The state-run news agency in Aden, aligned with the government-in-exile which is backed by the Saudi-led coalition, said Iran-linked rebels were using a nearby building as a storehouse for weapons.
Saudi-led air strikes on Yemen's capital Sanaa hit a warehouse near a girls' school on Sunday killing at least 13 children, and wounded more than 100, local medical officials said.
The Iran-aligned Houthi rebels, who seized control of the capital in 2014, said the Saudi-led coalition had targeted the warehouse with an air strike.
The coalition denied carrying out any strikes in the area.
The state-run news agency in Aden, aligned with the internationally-recognised government-in-exile, said rebels used the warehouse to store weapons.
Health officials said over 110 people were wounded in the attack.
Windows in the school building were shattered, panicking more than 2,000 students.
"The missile exploded and everybody started running. I was left behind and then fell over. They were stepping on me. Then someone came and helped me up. I still have a terrible pain in my knees," said Hadeel Mounir, an injured student.
"We went back to the classroom after the break. Then the enemy aircraft dropped the bomb and everyone wanted to run home. [I saw] four or five people trampled to death and eleven injured. It was very noisy and crowded in the school."
It is not the first time during Yemen's four-year civil war that a school has been bombed or targeted. A strike by the Saudi-led coalition on a school bus in August 2018 killed 51 people, including 40 children. Thousands of civilians have died in the conflict and hospitals have also been hit.
The coalition has been at war with the Houthis since 2015 in a conflict that has killed tens of thousands of people and pushed the Arab world's poorest country to the brink of famine.