Phillips 66 began shutting its 255,600 barrel-per-day (bpd) Alliance, Louisiana, refinery as Tropical Storm Sally was forecast to pass just west of the plant, 24 miles south of New Orleans.
Other refineries in east Louisiana were monitoring the storm, forecast to become a Category 2 hurricane with winds of 100 mph, early on Tuesday.
From Saturday, energy companies began shutting offshore production as they evacuated workers in the path of the storm, located 115 miles east-southeast of the mouth of the Mississippi River, the U.S. National Hurricane Center said.
Chevron Corp shut the Blind Faith and Petronius platforms and evacuated the workers, it said on Sunday.
Royal Dutch Shell Plc said it began shutting some of its offshore drilling operations on Sunday. Its offshore production was unchanged and all personnel remained on production platforms, company spokeswoman Cynthia Babski said.
Murphy Oil shut the Delta House platform in the path of Sally, the company said.
However, BHP Billiton does not plan to take workers from offshore facilities, a company spokeswoman said.
Equinor ASA shut the Titan platform and evacuated all workers on Saturday, a company spokesman said.
BP Plc evacuated non-essential workers from its Na Kika and Thunderhorse platforms, it said.
Other oil producers with drilling rigs and platforms in the area said they were monitoring the storm and ready for action as needed.
U.S. Gulf of Mexico offshore oil production makes up about 17% of U.S. crude oil and 5% of U.S. natural gas output. As much as 1.5 million barrels per day of oil output was shut last month as Hurricane Laura tore through the Gulf of Mexico.
Louisiana declared a state of emergency on Saturday and the city of New Orleans ordered a Sunday 6 p.m. CDT evacuation for residents outside its protective levees. Coastal Grand Isle also issued its third evacuation order since July.
Reporting by Erwin Seba and Gary McWilliams; Editing by Nick Zieminski and Clarence Fernandez