Scores more civilians were wounded in Sanaa on Sunday, according to a statement released by the UN that did not specify the cause of the casualties.
An AFP reporter on the ground said the injuries appeared to be the result of an explosion near a school in the city.
The coalition, which regularly carries out air strikes against the rebels, denied conducting any raids on Sanaa on Sunday.
Five students were among the dead, according to the UN, whose humanitarian coordinator for Yemen, Lise Grande, voiced alarm at the "terrible, senseless deaths and injuries".
"Every effort must be made to understand the circumstances that led to this tragedy," she said.
Yemen's Huthi rebels, locked in a war with Saudi Arabia and its military allies backing the government, on Sunday accused the coalition of bombing that they said killed more than 13 people and wounded 90.
The coalition, which has come under international pressure over its air strikes in Yemen, accuses the rebels of routinely using civilians as human shields.
The World Health Organization estimates nearly 10,000 Yemenis have been killed since 2015, when Saudi Arabia and its allies intervened to prevent the defeat of the government in the face of a rebel offensive.
Human rights groups say the real death toll is several times higher.
The conflict has pushed millions of Yemenis to the brink of mass starvation, in what the UN has called the world's worst humanitarian crisis.
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