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.
Rights groups have repeatedly criticised the coalition over the civilian casualties inflicted by its air strikes on rebel-held regions.
The Arab coalition launched a military campaign against the Iran-backed rebels in March 2015 in support of President Abedrabbo Mansour Hadi.
More than 7,000 people have been killed in the conflict.