It did not specify if those killed were civilians or troops.
A Saudi-led coalition launched air strikes on anti-government rebels in neighbouring Yemen on March 26, sparking sporadic border clashes with Saudi troops.
Fighting along the frontier has killed 12 soldiers and border guards but no civilian casualties have so far been reported.
"Three dead after Najran region attacked by mortar rounds and random Katyusha rockets from Yemen territory," the interior ministry said in a tweet sent late Tuesday.
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He said casualties occurred at a field hospital outside the city.
Saudi news channel Al-Ekhbariya showed footage of cars with windows blown out, chunks torn from pavements, a building peppered with shrapnel and one completely charred room with a hole in the ceiling.
Tuesday's assault was the first by the Huthis on an inhabited Saudi town.
It came as leaders of the six Sunni-dominated Gulf Cooperation Council states gathered for a special summit in Riyadh, with French President Francois Hollande in attendance.
But Shiite Huthi rebels reject holding talks in the Saudi capital. Iran, which denies accusations of arming the Huthis, has called for negotiations at a neutral location.
The United Nations says at least 1,200 people have been killed in Yemen since March 19.
The coalition says it has killed hundreds of rebels in northern Yemen.