A probe commissioned by the coalition claimed that the closest targets hit by warplanes were 10 kilometres (six miles) away from the school
The headmaster and two other staff members were among those killed in the air raid in the district of Nihm, northeast of the capital Sanaa, which also left 13 wounded, the sources said.
A medical source at Kuwait Hospital in Sanaa confirmed the casualty toll.
A government military official said the school was hit by two missiles by mistake, accusing the Shiite Huthi rebels of keeping armoured vehicles nearby.
The rebels' saba.ye news website said eight people had been killed and 15 wounded.
Human rights groups have repeatedly criticised the coalition over the civilian death toll from the bombing campaign it launched in March 2015.
In August, an air strike on a Koranic school in Saada province, a rebel stronghold in the far north, killed 10 children and wounded 28 other people, prompting a UN call for a swift investigation.
But a probe commissioned by the coalition claimed that the closest targets hit by warplanes were 10 kilometres (six miles) away from the school.
Amnesty International and Human Rights Watch have called on Washington, London and Paris to stop their deliveries of bombs and other weapons to Riyadh because of concerns over civilian casualties.
More than 7,000 people have been killed in Yemen since the coalition launched its intervention, many of them civilians killed in its air strikes.
Washington has scaled back its logistics and intelligence support for the coalition's air war because of concerns about its targeting.