Major General Turki al-Maliki, spokesman for the Saudi-led military coalition supporting Yemen's internationally recognised government, said Thursday's attack in southern Najran Province injured seven Saudis, one Yemeni, two Egyptians and one Pakistani national.
The victims included a four-year-old child who suffered second-degree burns.
Maliki accused the Iran-aligned Houthis of indiscriminately shelling civilian areas in violation of international humanitarian law and said the coalition would continue taking all necessary measures to protect civilians.
There was no immediate comment from the Houthis or Iran on the coalition's statement, as the five-month-old US-Israeli war with Iran has complicated Saudi Arabia's security calculations.
Iran has attacked the kingdom because it hosts US military facilities.
Meanwhile, Riyadh's decade-old conflict with the Tehran-aligned Houthis has become increasingly entangled with the wider war, as Houthi actions, such as a Red Sea blockade that has disrupted Saudi oil exports, have raised the stakes of the broader regional confrontation.
A senior Saudi official, speaking on condition of anonymity, said Saudi, US and other Middle Eastern countries' intelligence found the Houthis and Iraqi militias under the supervision of Iran's Islamic Revolutionary Guard Corps could soon launch co-ordinated attacks on Saudi civilian sites including energy infrastructure, ports and airports.
Riyadh is seeking to deepen security co-operation with key allies while warning of an expanding regional threat from Iran-backed groups.
Turkey, Saudi Arabia and Pakistan were due to sign a defence agreement in the kingdom on Friday, two regional sources with direct knowledge of the matter told Reuters.
Details of the agreement were not immediately available.
Saudi Arabia already has a defence co-operation agreement with Pakistan. Pakistani Prime Minister Shehbaz Sharif arrived in the kingdom on Thursday, while Turkish President Tayyip Erdogan was due to arrive on Friday.
The Saudi official said the reported threats were alarming as Riyadh continued to support de-escalation and a negotiated settlement of the conflict with Iran, adding that mediation efforts appeared to be moving "in the right direction". He said the planned attacks could be intended to disrupt the diplomacy.
The official said Saudi-US cooperation remained "very high" at all levels, including operationally with US Central Command, and said Saudi Arabia was prepared to take all necessary measures to respond to any aggression.
The Houthis on Tuesday claimed responsibility for an attack on Najran airport, part of a broader escalation in which the Iran-aligned group has struck Saudi military, infrastructure and shipping targets.
On July 29, Saudi Arabia said it carried out strikeswith US Central Command against Iran-backed groups in Iraq after blaming them for drone attacks on its oil facilities. Iraqi militias said they would respond to the Saudi strikes.
