Energy companies were assessing the health of refineries, pipelines, petrochemical plants and offshore oil platforms along the central Gulf of Mexico on Monday, the day after Ida struck Louisiana as a powerful Category 4 hurricane.

Widespread flooding and power outages affecting more than one million customers across the state could leave gasoline makers along the banks of the Mississippi River scrambling to restart operations after they assess damages this week, analysts said.

Companies including Marathon Petroleum Corp. , Valero Energy Corp. , Phillips 66 and Royal Dutch Shell PLC shut roughly 8% of the nation’s refining capacity ahead of the storm, while Colonial Pipeline Co., operator of the largest U.S. fuel pipeline, closed two lines that carry fuel from Houston to Greensboro, N.C. Exxon Mobil Corp. had shut some units at its chemicals and refining complex in Baton Rouge, but said there was no significant storm damage.

“There’s no clarity,” around power supplies in the region as of yet, said Tom Kloza, global head of energy analysis for Oil Price Information Service, or OPIS. “If they say the southeastern parishes that house a lot of big refineries aren’t going to be back on the grid for weeks, it’s a much more serious event.”

Companies in coming days will work carefully to determine whether flooding, wind or other impacts of Ida caused any damage to the integrity of their facilities or posed any environmental threats.

Hurricane Ida hit Louisiana as a Category 4 storm and knocked out power to the entire city of New Orleans. The storm is testing a $14.6 billion system including levees and flood walls, while threatening hospitals overwhelmed with Covid-19 patients. Photo: Eric Gay/Associated Press The Wall Street Journal Interactive Edition

Major storms have caused severe problems for industrial plants in the past, such as in 2017, when flooding from Hurricane Harvey led to a failure of a main power source for a plant owned by chemical maker Arkema SA near Houston. The plant caught fire and exploded after the storm.

In 2005, following Hurricane Katrina, hundreds of thousands of gallons of oil spilled from a storage tank at a refinery, then owned by Murphy Oil Corp. , with some leaking into neighborhoods near New Orleans.

Marathon is developing a timeline to restart its 565,000 barrel-a-day refinery at Garyville, La., a spokesman said. Exxon said its Baton Rouge plant will start returning operations to normal once it confirms it has access to feedstocks and third-party utilities “to stabilize our systems.”

Phillips 66 said its 255,000 barrel-a-day refinery in Belle Chasse, La., was still closed Monday evening, and that the facility had taken on water. It planned to survey Ida’s impact “when it is deemed safe to do so.”

Gasoline futures rose as much as 4.3% overnight but pared gains and were up about 1.6% Monday. Average U.S. gasoline prices were expected to register little impact from the storm, likely only rising 5 to 10 cents a gallon, analysts said, well below price surges that followed Katrina and Harvey.

The average U.S. price for a gallon of regular rose less than 1 cent to about $3.15 Monday, with prices roughly flat in Louisiana, according to AAA.

Still, prolonged refinery shutdowns caused by flooding and other delays in the fuel supply chain could push pump prices higher, by as much as 15 to 25 cents a gallon nationally in the worst-case scenario, said Patrick De Haan, head of petroleum analysis at fuel and price tracker GasBuddy.

“Refineries have adapted to wind speed,” Mr. De Haan said. “What they can’t do is build and plan for 12 to 24 inches of rain.”

Data collected by GasBuddy showed about 10% of gasoline stations in the Baton Rouge area were out of fuel over the weekend, as were 7.5% near New Orleans. Those figures are expected to worsen sharply as Ida passes, and it could take a week or two for regional supplies to recover in the state’s hardest-hit areas, Mr. De Haan said.

Ships anchored in the Mississippi River on Saturday in Convent, La., ahead of Hurricane Ida.

Photo: Luke Sharrett/Bloomberg News

All told, roughly 4.4 million barrels of refining capacity was projected to have been in Ida’s path, according to S&P Global Market Intelligence, roughly a quarter of the U.S. total. The firm also estimated petrochemical facilities with a combined 6.5 million tons a year of capacity for ethylene, a key ingredient for plastics, were vulnerable to the storm.

Dow Inc., which owns petrochemical plants in Louisiana, said it shut manufacturing operations over the weekend. Other companies with chemical operations that were in Ida’s path included Westlake Chemical Corp. and NOVA Chemicals Corp., according to S&P Global Market Intelligence.

Adding to the uncertainty is the recovery time for major power failures across the state. Entergy Corp. , a major Louisiana power supplier, said all eight transmission lines feeding power into New Orleans were down Sunday, causing generation to come offline and leaving the city in the dark. Power was out for more than one million customers in Louisiana on Monday, according to data from poweroutage.us.

Entergy said it had crews ready to mobilize from at least 22 states for restoration work, but warned the outages could last weeks in the areas hardest hit by the storm. It will take days to determine Ida’s damage to its power grid in New Orleans, “and far longer to restore electrical transmission to the region,” the company said on social media Monday.

Entergy shut down a nuclear plant 25 miles west of New Orleans on the Mississippi River ahead of the storm. It lost off-site power on Sunday and was relying on emergency diesel generators, according to a regulatory notice.

Colonial said it expected to bring its two key lines back online Monday evening, following damage assessments and safety checks. Colonial moves more than 100 million gallons of fuel a day on its 5,500-mile pipe network from the Gulf Coast to Linden, N.J.

The Plantation Pipeline also ships gasoline from the region to the East Coast and was still operating, but Kinder Morgan Inc. said its terminal in Baton Rouge had lost power, which could affect the pipeline by Monday or Tuesday. The company was checking on the extent of damage to its facilities in Baton Rouge and said the power company was determining the repairs needed to restore power.

Pipeline operator Enbridge Inc. said it mobilized crews to assess any damage to its facilities or nearby areas.

Offshore oil companies in the U.S. waters of the Gulf of Mexico, which account for about 17% of U.S. oil production and 5% of natural-gas output, had almost completely shut off flows from their production platforms and had evacuated more than half of them, according to a Monday report from the Bureau of Safety and Environmental Enforcement.

That took about 1.72 million barrels a day of oil production and 2.1 billion cubic feet a day of natural-gas output offline.

Shell said late Sunday it scheduled a flyover to assess the storm’s impact to its four major offshore platforms Monday afternoon.

Write to Collin Eaton at collin.eaton@wsj.com and Jennifer Hiller at jennifer.hiller@wsj.com