The school's headmaster and two children were among those killed, medical and military sources said. The death toll was confirmed by a medical source at Sanaa's Kuwait hospital.
A government military official said the school was hit by two missiles by mistake, accusing the Houthi rebels of keeping armoured vehicles nearby.
Since it began airstrikes in support of Yemen's embattled government, the Saudi-led Arab coalition has come under fire from rights groups and the United Nations over alleged human rights violations and war crimes.
In August, 10 children and 28 others were wounded when a religious school was struck in the northern Saada province. This prompted the UN to launch a swift investigation into the airstrike.
Last year, the UN also briefly placed the Saudi-led coalition on a blacklist of nations and groups who violate the rights of children in war, due to the hundreds of children that have been killed in coalition airstrikes.
This decision was later rescinded following diplomatic pressure from the kingdom.