The Islamic school said in a statement that the strike in Saada, deep in the Houthis' northern heartland, was part of raids that have resumed against the rebels after peace talks collapsed earlier this month.
Aid group Doctors Without Borders condemned the attack on social media, saying that all ten killed and 28 injured were between eight and 15 years old. The school released some of the names of those killed.
The war has left a security vacuum throughout parts of the country.
Both al-Qaida and its rival militant group, the Islamic State group, have exploited the turmoil and expanded their footprint in the country's southern region.
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Separately, lawmakers convened at Yemen's parliament for the first time since the Houthis disbanded the body in early 2015, aiming to consolidate power inside the country after the Shiite rebels and the party of former president Ali Abdullah Saleh named a joint body to rule the parts of the country they control.
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The coalition, meanwhile, said Saudi air defences
yesterday intercepted a Scud missile fired from Yemen.
And the Saudi civil defence said six foreign workers at a water-bottling plant in Najran -- three Indians, two Bangladeshis and a Nepali -- were wounded when a factory was hit in a rebel bombardment from across the border.
Around 100 Saudi soldiers and civilians have been killed inside the kingdom's borders since last March.
The coalition has also been backing government forces fighting Sunni jihadists who have exploited the conflict to gain ground in southern Yemen.