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.
UAE authorities on Monday issued mobile phone alerts in Dubai and Abu Dhabi warning of the possibility of missile attacks.
Monday's strike was not the first time Fujairah's energy infrastructure had been in the crosshairs.
A drone attack on March 14 had previously hit the Port of Fujairah, triggering fires and the suspension of some oil-loading operations.
Fujairah has been key to UAE oil exports during the Iran war as it sits at the end of the Abu Dhabi Crude Oil Pipeline, which carries crude from inland fields to the Gulf of Oman, bypassing the Strait of Hormuz.
This has allowed the UAE to continue shipping oil to global markets even as the waterway remained under threat.
US Admiral Brad Cooper, the head of Central Command, said on Monday that the US military destroyed six Iranian small boats and intercepted Iranian cruise missiles and drones as the US launches 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.
