The missile was deliberately launched towards Najran to target civilian areas, but it was intercepted and destroyed by the Brigades "Patriot" in the sky of Najran, said Malki.
It marks the latest missile fired by Houthi forces, in Yemen, who are now in the thick of a stand-off with Saudi Arabia, widely described as a proxy war.
Al Masirah television, controlled by the Houthis, said the second missile was launched against forces loyal to President Abd Rabbo Mansur Hadi along the western coast of Yemen.
Saudi Arabia has repeatedly accused its regional rival Iran of arming the Shia Houthis, but Tehran denies the allegations.
"This hostile act by the Iran-backed Houthis proves the Iranian regime remains implicated in supporting the armed Houthis", Maliki was quoted by Saudi state news agency SPA as saying.
The scattered fragments of the missile caused minor damage to a private property, while no injuries were reported.More news: Nintendo Switch becomes USA fastest-selling console
Last December, the group said it had targeted a palace used by Saudi King Salman bin Abdulaziz.
A spokesman for the Saudi-led military alliance fighting the Huthis in Yemen did not immediately respond to a request for further details.
But despite the coalition's superior firepower, the rebels still control the capital and much of the north.
More than 8,750 people have been killed since the coalition intervened, according to the World Health Organization.
The United Nations calls Yemen the world's worst humanitarian crisis, with 8 million people on the brink of starvation.