The group said it had struck Riyadh airport, where witnesses saw smoke billowing from a plane, and it warned workers to stay away from energy plants.
Saudi officials said debris from an intercepted missile had hit a kindergarten and medical complex.
The Houthi movement say they are targeting the kingdom over its support for government forces in Yemen's reignited civil war.
Saudi Arabia says it is backing an offensive by Yemen's United Nations-recognised government to take back territory from the Houthi rebels.
The conflict has added new chaos to a region already aflame and threatens to draw other states into gruelling mountain fighting - with Syria now considering deploying troops to assist Saudi Arabia.
The kingdom has pushed for support from allied countries, including Turkey and Pakistan, even if only in a logistical or defensive capacity, as it tries to reverse Houthi gains in southwest Yemen, by the southern entrance to the Red Sea.
Those requests have taken on more urgency since Saudi authorities said on Wednesday that three people had been killed this week in strikes on Riyadh airport and Abha airport in the southwest.
The Houthis have made Saudi airports a major focus of their strikes, and the Saudi-led coalition fighting in Yemen said it had destroyed two ballistic missiles launched by the group towards Riyadh and another towards Khamis Mushayt, home to a major air base.
The smoke at Riyadh airport on Thursday was rising from a stationary aircraft that was believed to be empty, three people briefed on the matter said.
The fire had since been put out, they said.
There was no immediate confirmation from Saudi authorities on the Houthi claims of ballistic missile attacks on Riyadh airport and the cause of the smoke billowing from the plane was not immediately clear.
However, the flight tracker FlightRadar24 indicated numerous delayed arrivals and departures at Riyadh's King Khalid International Airport on Thursday.
The airport advised travellers to contact airlines to check the status of flights before trying to travel.
Saudi authorities said debris from an intercepted Houthi missile had landed in Riyadh, causing damage to a kindergarten and a medical clinic complex, state media reported.
Riyadh is due to host a major meeting of energy policy makers, the WPC Energy Congress, this week.
