The child died instantly while the rest of the family were taken to hospital, according to Lieutenant Colonel Ali bin Omair al-Shahrani, who was quoted by the official SPA news agency.
Shiite Huthi rebels in Yemen have intensified cross-border rocket attacks since late last year.
Around 90 civilians and soldiers have died from shelling and skirmishes in Saudi border regions since March when a Saudi-led military coalition began air and ground action in Yemen.
In Yemen, more than 5,800 people have been killed since March, about half of them civilians, and 27,000 wounded, according to the United Nations.