Saudi Arabian state television said that the Houthis fired two missiles toward the country late Sunday and the Saudi air defence forces succeeded in intercepting one over Riyadh, and another over Jazan in the Saudi Arabian border with Yemen.
The intended target of the Burkan H2 missile was reportedly the King Khalid global airport in Riyadh.
He also praised Houthi forces for firing several missiles against the targets in Saudi Arabia on Sunday.
The attacks against the Saudi positions came just ahead of Monday that marks the anniversary of the start of an ongoing devastating war on Yemen.
Riyadh has been the target of similar attacks, but this is the first one that has resulted in a fatality.
Both parties in the Yemen conflict have drawn harsh condemnation for failing to protect civilians in a war that has claimed almost 10,000 lives and pushed the country to the brink of starvation. After the November 4 missile strike, the Kingdom's foreign minister accused Hezbollah, the Lebanese Shiite militant and political group that is aligned with Iran, of smuggling missile parts into Yemen.
The European Union on Tuesday condemned the Houthi barrage rocket attack on Saudi Arabia that killed one person and injured two others.
Allies of Saudi Arabia have also accused Tehran of providing the Huthis with missiles, and Britain on Monday urged Iran to "stop sending in weapons which prolong the conflict, fuel regional tensions, and pose threats to worldwide peace and security".
The United Nations is making a fresh push for peace talks in Yemen, where the coalition acted to support the internationally-recognized government after the Huthis seized the capital. "The missiles launched against Saudi territory were smuggled from Iran", coalition spokesman Turki al-Malki told reporters on Monday.
Qassemi also referred to the threatening statements of a Saudi military commander about Iran and said it goes without saying that such warmongering and irresponsible statements can be followed up legally and internationally.
The three-year conflict pits a coalition of Sunni Arab states friendly to the West against the Houthis, a Shi'ite armed movement sympathetic to Iran.
Meanwhile, the US provides logistical support and weaponry to the Saudi-led coalition, which has been criticized for its airstrikes on Yemen killing civilians, as well as a blockade of Yemeni ports that has brought the country to the edge of starvation.
Since Saudi Arabia entered the proxy war with Iran, around 10,000 people have been killed and 53,000 wounded in Yemen, triggering what the United Nations describes as the world's worst humanitarian crisis.