The claim came as witnesses reported several explosions across the Saudi capital, a day after a separate Houthi drone attack on the same airport killed one person and caused flight delays that continued into Thursday.
Operation Yemen Dawn, backed by 100 Saudi coalition aircraft, retook the town of Dhubab just north of the strait, as the Houthis claimed they struck Riyadh's international airport, an oil refinery and military bases across Saudi Arabia, and Pakistan and Turkey agreed to deploy troops to the kingdom.
The Saudi-led coalition said a drone hit the Taibah electricity distribution station, which supplies power to the Prophet's Mosque, one of Islam's holiest sites. The Houthis denied the claim, stating it was a "lie" to back previous allegations against the group.
The Houthis declared a naval blockade of Saudi Arabia in July and have since been launching increasing attacks on Saudi cities and shipping, further heightening tensions in the Middle East.