The Saudi-led coalition, which has been at war with the Iran-aligned group since 2015, did not immediately confirm the attacks.
Yahya Sarea, a spokesman for the Houthi military, said the group used a Dul-Faqqar ballistic missile and three Samad3 drones to attack an important target in Riyadh, without giving more details. The group have attacked Riyadh several times before.
"The attacks are a response to the enemy's permanent escalation and its continuing blockade against our country," Sarea said in a statement posted on Twitter.
He promised more attacks if Saudi Arabia "continues its aggression" against Yemen.
The Houthis took over the Yemeni capital Sanaa and most cities in 2014 after ousting the Saudi-backed government of Abd-Rabbu Mansour Hadi.
The Western-backed coalition that Saudi Arabia leads intervened to try to restore Hadi to power but the war, which has killed 100,000 people, has been stuck in a stalemate for years.The conflict has led to what the United Nations describes as the world's worst humanitarian crisis.