Yesterday's attack on Najran left one Saudi citizen and two Indian workers dead, according to a civil defence spokesman quoted by the official SPA news agency.
India's consul general in Jeddah, B.S. Mubarak, confirmed that two Indians from the southern state of Tamil Nadu were killed in the attack near a museum on the edge of Najran.
Another Indian was killed in shelling in the border region about six months ago, he said.
One of the missiles was intercepted by Saudi air defences, while the other struck a desert area east of Najran, the coalition said without reporting any casualties in that incident.
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On Thursday the civil defence agency said a civilian had been wounded in the Jazan border region by shelling from Yemen.
The ceasefire has been repeatedly breached since it came into force as UN-sponsored talks opened Tuesday in Switzerland.
More than 5,800 people have been killed -- about half of them civilians -- and over 27,000 wounded in Yemen since then, according to the UN.
In Saudi Arabia, more than 80 people, most of them soldiers and border guards, have died in shelling and cross-border skirmishes since March.