The Houthis also said they had attacked Saudi military aircraft and repelled an advance by Saudi-backed forces near the Bab al-Mandab Strait, an important Red Sea shipping route.
Yemen's Iran-aligned Houthis said on Tuesday they had hit Saudi Arabia's Ras Tanura oil refinery, the biggest in the kingdom, with a ballistic missile.
The Houthis also said they had attacked Saudi military aircraft and repelled an advance by Saudi-backed forces near the Bab al-Mandab Strait, an important Red Sea shipping route.
Intensifying hostilities between the Houthis and Saudi Arabia have further disrupted oil supplies and heightened the risk of a wider regional conflict, eight months since the Iran war began.
The Houthis' military spokesperson, Yahya Saree, said the strike on the Ras Tanura refinery had caused a fire at the complex, which also includes a shipping terminal and is located on the Gulf, west of the Strait of Hormuz.
Saree also claimed that the Houthis had hit the Saudi Ministry of Defense with a ballistic missile and Abha International Airport with a drone.
Saudi authorities did not confirm any of the strikes.
Ras Tanura, which has a capacity of 550,000 barrels per day, was shut for a period in the early months of the Iran war as a precautionary measure.
Nearly all Saudi Arabia's oil exports flow through two main ports: Ras Tanura in the Gulf and Yanbu on the Red Sea, both of which the Houthis have attacked in the past.
Bloomberg News cited a person familiar with the matter as saying Saudi Arabia had contained a fire near Ras Tanura's terminal.
Houthis claim to have hit two military transport jets
The Houthis said they had attacked two military transport jets at Najran Airport and an airbase in Khamis Mushait. There was no immediate Saudi confirmation of the attacks.
On Tuesday afternoon, civil defense authorities briefly issued an air raid alert in the Saudi capital Riyadh.
The Saudi-led coalition fighting the Houthis in support of Yemen's internationally recognized government said it had intercepted and destroyed two ballistic missiles launched by the Houthis towards Riyadh.
The Houthis said they had repelled an advance by forces they described as Saudi-backed from the southern approaches to the Bab al-Mandab Strait.
Saudi-backed Yemeni government forces earlier this month pushed the Houthis out of coastal areas they had seized in September, loosening the group's grip on a vital Red Sea oil route.
Houthi media claims Saudi struck Mocha
Houthi-affiliated Al Masirah TV reported Saudi strikes on the Yemeni city of Mocha. There was no immediate Saudi confirmation.
The fighting has shattered a 2022 UN-brokered truce between the coalition and the Houthis, who control the Yemeni capital Sanaa.
On Monday, Saudi Arabia, Turkey and Pakistan met Iranian officials in Tehran to try to reduce regional tensions.
Parliament in Egypt, which has said it is considering joining the three countries in a mutual defence pact, authorised Egypt's military on Monday to help defend Saudi Arabia if asked.