The storm had already claimed the lives of at least two people in China's Hainan and 16 people in the Philippines
Production at the 200,000 barrel-per-day (bpd) Shuaiba refinery was not affected, the company said.
The fire broke out in the early hours of Monday during maintenance operations, it said in a statement carried by the state KUNA news agency.
Firefighters quickly doused the blaze, which caused little damage. An investigation has been launched.
Shuaiba, 80 kilometres (50 miles) south of the capital, is the smallest of Kuwait's three refineries, which between them have a production capacity of 920,000 bpd.
Kuwait, OPEC's fourth largest oil producer, pumps some 2.58 million bpd. The Gulf state announced plans in February to increase its current total output capacity from 2.7 million bpd to four million bpd by 2020.
The storm had already claimed the lives of at least two people in China's Hainan and 16 people in the Philippines
Dubai Police have asked drivers to be extra cautious
The former all-rounder has returned to cricket during the past year after a horrific car crash at the end of 2022
Dubai Police have asked drivers to be extra cautious
The country has set a new Guinness World Record by creating the largest falcon hood, beating the previous record of 1.65 metres
Hamas' health ministry said that 94,616 people have been wounded since the conflict began on October 7
In most Islamic countries, including the Gulf countries, the Prophet's birthday is observed on 12 Rabi’ Al-Awwal 1444
Traffic will be diverted to the opposite side during this period