The rebels fired 10 Badr-1 ballistic missiles at Jizan airport, killing and wounding dozens, the group's military spokesperson said in a statement on Sunday.
The Saudi-led coalition fighting the Houthis said that it had intercepted and destroyed at least six ballistic missiles fired by the group targeting civilians in the city of Jizan in the southwest of the kingdom.
"The Houthi militias continued targeting of civilians through drones and ballistic missiles ... is an act of aggression and terrorism and a war crime according to international human law," the coalition spokesman, Colonel Turki al-Malki, said in a statement carried by Saudi state news agency SPA.
There were no immediate details about any casualties or damage.
The Houthi attack is part of an escalation of cross-border assaults in the four-year-old conflict between the Houthis and the coalition, led by Saudi Arabia and the United Arab Emirates and backed by Western powers.
The Houthi rebels, who control most urban areas of Yemen including the capital, Sanaa, have in recent months stepped up attacks against targets in Saudi Arabia.
In response, the coalition has targeted military sites belonging to the group, especially around Sanaa.
The coalition intervened in Yemen in 2015 in a bid to restore the internationally recognised Yemeni government that had been overthrown by the Houthis in late 2014.
Since then, the conflict has killed tens of thousands of people and pushed millions to the brink of famine. The United Nations has described the conflict in Yemen as the world's worst humanitarian crisis.
The escalation of violence threatens a UN-sponsored deal for a ceasefire and troop withdrawal from the port city of Hodeidah, which became the focus of the war last year when the coalition tried to seize the port, the Houthis' main supply line and a lifeline for millions of Yemenis.