"They fired one missile, a Katyusha... At the time of Friday prayer," Brigadier General Ahmed al-Assiri, the coalition spokesman, told AFP.
Assiri initially said two people had died in the attack.
The incident came two days before Yemen's exiled government and rebel forces are set to hold talks in Geneva sponsored by the United Nations in an effort to end the war that has killed more than 2,000 people.
On the Saudi side of the frontier at least 39 people -- civilians and troops -- have now lost their lives in shelling and border skirmishes since March 26, when the coalition began bombing Iranian-backed Huthi rebels in Yemen.
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Last Saturday the coalition said it shot down a Scud missile fired from Yemen and Assiri said the alliance is still hunting others that might be in rebel hands.
"We are not at zero risk," he said.
The coalition made targeting rebel missile capabilities a priority when it launched its aerial campaign.
"We destroyed most of them," Assiri said, adding that 300 missiles of various types belonged to the Yemeni army before the war.
Huthi rebels obtained government weapons when they seized the capital Sanaa late last year before advancing into other parts of the country.
About 10 percent of the rebel missile arsenal has yet to be located, he said.
"We work hard to find them. It is not an easy task.