The Iran-aligned Houthis in Yemen said they fired dozens of missiles and drones on Monday at a Saudi air base in Khamis Mushait, near the border, hitting aircraft hangars, radar systems, runways and ammunition depots.
They described the attack as retaliation for hundreds of Saudi air strikes on Yemen in recent days.
Saudi authorities announced brief emergency alerts there and in three other southern cities which have previously come under Houthi fire.
The Houthis launched a lightning advance last week in Yemen, culminating in the seizure of an island in the mouth of the Red Sea on Friday.
A separate attack that day, which Riyadh blamed on Iran-backed fighters in Iraq, knocked out Saudi Arabia's east-west pipeline, the main route for Middle East oil bypassing the blockaded Strait of Hormuz.
Crude oil prices rose more than three per cent on Monday, when the market reopened after the weekend, while the politically sensitive average retail price of diesel in the United States hit a record high above $US6.23 a gallon.
Traders say the closure of the Saudi pipeline could cut off as much as four per cent of global oil supply unless it is reopened within days.
Images from space show sections of the pipeline damaged by blazes.
Riyadh has not given a firm estimate for how long it will be shut.
Oman had been due to host a meeting on Monday with Iran and Gulf states to discuss negotiations aimed at reopening Hormuz, the world's most important oil shipping lane, largely closed since the US and Israel attacked Iran at the end of February.
But Omani Foreign Minister Sayyid Badr Albusaidi announced overnight that the meeting had been postponed "in the interests of consensus".
Iran said the postponement was at the request of Saudi Arabia.
Meanwhile, Iran issued a list of 77 ships it said had violated its protocols for operating in the Strait of Hormuz.
Any ship on the list would face "restrictions on future passages, including fines, detention, or confiscation", and other ships that assisted them by accepting transfers of cargo would be added to the list.
The upsurge of fighting in Yemen poses a dilemma for Washington, which is under pressure to aid its Saudi allies but anxious not to expand the costly war to a new theatre.
Saudi Arabia has led an Arab coalition battling the Houthis for more than a decade after the mountain fighters captured Yemen's capital in 2014.
The war there had largely been quiet under a ceasefire for the past few years, but fighting has resumed, with the Houthis driving back forces from a Saudi-backed government based in the south.
Thousands of Yemenis have fled inland from the coast to escape fighting as the Houthis swept into cities including the historic Red Sea port of Mocha last week.
On Friday, the Houthis captured Perim Island, inside the Bab el-Mandeb, the "Gate of Tears" strait, at the mouth of the Red Sea.
US President Donald Trump is under pressure to end the war to relieve the global energy shortage and lower prices that are hurting the fortunes of his Republican Party before midterm elections in November.
Three sources have told Reuters that Washington has rebuffed pleas from Saudi Arabia's Crown Prince Mohammed bin Salman to intervene in Yemen.
Trump confirmed at the weekend that he had spoken to the prince, and said the Houthis had also phoned asking Washington to keep out of the dispute.
Trump, who attended a golf tournament at one of his resorts in Ireland, said he expected the Iran war to end shortly after the elections in November, after which the price of oil would "drop like a rock".
