"This hostile act by the Iran-backed Huthis proves the Iranian regime remains implicated in supporting the armed Huthis," the kingdom's state news agency SPA quoted coalition spokesman Turki al-Maliki as saying.
Riyadh earlier said Saudi air defences had intercepted a ballistic missile over the southern province of Najran, hours after the Huthis announced they had launched an attack on the kingdom.
Maliki said Friday's attack "deliberately targeted densely populated civilian areas" and had caused minor damage to the property of a Saudi citizen.
No casualties were reported.
Saudi Arabia and its allies, who support the Yemeni government in its fight against the Huthis, have long accused Iran of backing the rebels.
In December, Riyadh warned "Iranian-manufactured ballistic weapons" threatened the kingdom's security following a foiled ballistic missile attack from Yemen.
The Saudi-led coalition intervened in support of Yemeni President Abedrabbo Mansur Hadi's government in March 2015, after the Huthis seized the capital Sanaa.
The rebels still control the capital and much of the north of the country.
More than 8,750 people have been killed since the coalition intervened, according to the World Health Organization.
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