A huge plume of black smoke could be seen rising over the Red Sea city where the Saudi Arabian Formula One Grand Prix is taking place this weekend, an eyewitness said.
The coalition statement on state media said the fire had been brought under control.
Flames could still be seen in live footage aired by the Saudi-owned Ekhbariya television channel.
The Saudi energy ministry said the kingdom strongly condemned the "sabotage attacks", reiterating it would not bear responsibility for any global oil supply disruptions resulting from such actions, state news agency SPA reported, citing an official in the ministry.
The ministry blamed Iran for continuing to arm the Houthis with ballistic missiles and advanced drones, stressing the attacks "would lead to impacting the Kingdom's production capacity and its ability to fulfil its obligations to global markets".
Tehran denies arming the Houthis.
There was no immediate comment from Aramco.
Formula One CEO Stefano Domenicali told drivers and team bosses the weekend's grand prix will go ahead as planned, according to a source familiar with the matter.
The Iran-aligned Houthis, who are battling the coalition led by Saudi Arabia, have intensified attacks on energy facilities in the kingdom, the world's largest oil exporter.
Houthi military spokesman Yahya Sarea said the group launched missiles on Friday at Aramco's facilities in Jeddah, and drones at the Ras Tanura and Rabigh refineries, and said it had also targeted "vital facilities" in Riyadh, the capital.
Saudi state media earlier said the coalition had foiled a string of Houthi drone and rocket attacks.
Saudi air defences also destroyed a ballistic missile launched towards Jizan, which caused a "limited" fire at an electricity distribution plant.
The Houthi escalation comes as the United Nations special envoy tries to secure a temporary truce for the Muslim holy month of Ramadan that starts in April, and ahead of Riyadh hosting Yemeni parties for consultations later this month.
Washington condemned the attacks on its ally Saudi Arabia, and said it would continue to work with Riyadh to strengthen its defences while working for a durable resolution to the conflict in Yemen.
"The attacks are unacceptable and have also affected Saudi infrastructure as well as schools, mosques and workplaces" and endangered civilians including US citizens," State Department deputy spokeswoman Jalina Porter told reporters on a briefing call.
Last weekend a Houthi assault on the kingdom caused a temporary drop in output at a refinery and a fire at a petroleum products distribution terminal.
On March 11, the group targeted a refinery in Riyadh, causing a small fire.
The coalition intervened in Yemen in March 2015 after the Houthis ousted the Saudi-backed government from the capital, Sanaa, in late 2014.
The conflict, widely seen as a proxy war between Saudi Arabia and Iran, has killed tens of thousands of people and pushed Yemen to the brink of famine.
The Houthis say they are fighting a corrupt system and foreign aggression.
