The ministry of energy and mines said the fire, which broke out in one of the refinery's warehouses, had been brought under control.
"The cause is under investigation," the ministry said in a post on X.
The fire occurred not far from where two oil tankers were moored.
Two Mexican navy ships arrived at the same harbor Thursday with more than 800 tons of much-needed humanitarian aid.
Cuba has risked being plunged into darkness since US President Donald Trump vowed to starve the communist-ruled nation of oil.
The Caribbean country of 9.6 million inhabitants lost its main oil supply line when Trump last month ordered the abduction of Nicolas Maduro, the long-term leader of Cuban ally Venezuela.
Trump said no more Venezuelan oil would go to Cuba, and also threatened tariffs for any other country stepping in with crude supplies.
The island, under a US trade embargo since 1962, has for years been mired in a severe economic crisis marked by extended power cuts and shortages of fuel, medicine and food.
No foreign fuel or oil tanker has arrived in Cuba in weeks, experts in maritime transport tracking have told AFP.
Emergency measures kicked in this week to conserve Cuba's fast-dwindling fuel stocks. The government shuttered universities, reduced school hours and the work week, and slashed public transport as it limited fuel sales.
Staffing at hospitals was also cut back.
The United Nations said Friday it was deeply alarmed by the crisis unfolding in Cuba.