Civil defence teams were deployed immediately to contain the blaze at the Fujairah Oil Industry Zone, the Fujairah Media Office said in a statement, adding that three Indian citizens were moderately injured in the attack and taken to hospital.
The UAE defence ministry said on X that its forces had intercepted three missiles, with a fourth falling into the sea.
Iran's Revolutionary Guards Navy issued a map it said showed an expansion of areas under Iranian control near the Strait of Hormuz, encompassing the UAE ports of Fujairah and Khorfakkan as well as the coast of the Umm Al Quwain emirate, Iranian news agencies reported.
The drone attacks shattered a period of relative calm in the United Arab Emirates since a Pakistani-mediated ceasefire between the United States and Iran took effect on April 8, pausing more than two months of intense fighting in the Gulf region.
During the period of intense conflict, the UAE said it had intercepted and destroyed thousands of drones and missiles.
US Admiral Brad Cooper, the head of United States Central Command, said on Monday that the US military destroyed six Iranian small boats and intercepted Iranian cruise missiles and drones as the US launched an operation to free up shipping through the Strait of Hormuz.
Cooper said he "strongly advised" Iranian forces to remain clear of US military assets as it launches the operation.
He said a US blockade of Iran, which prevents ships from going to Iran or departing Iranian territory, also remains in effect and was exceeding expectations.
US President Donald Trump announced his new "Project Freedom" mission on social media overnight to enable stuck ships to travel through the strait, the first apparent attempt to make use of naval power to unblock the world's most important energy shipping route.
The US military said two US merchant ships made it through the strait, without saying when.
Iranian authorities denied any such crossings had taken place.
Iran also denied that US forces in the region had destroyed six small Iranian boats.
South Korea reported one of its merchant ships suffered an explosion and fire inside the strait.
Maritime security agency UKMTO reported two ships had been hit off the coast of the UAE, and the Emirati oil company ADNOC said one of its empty oil tankers was hit by Iranian drones.
The UAE said Iranian drone and missile attacks on its territory marked a serious escalation and it reserved the right to respond.
Its government also said that it was implementing distance learning for school students for safety reasons.
In Oman, authorities said a residential building near the strait "was targeted," resulting in two foreign workers wounded, four vehicles damaged and nearby windows shattered.
The report carried by state-run media did not provide further details.
