In a statement, Motiva declined to say how long its Port Arthur refinery would remain offline, saying it would start the process once local flooding receded.
"Given the unprecedented flooding in the city of Port Arthur, it remains uncertain how quickly the flood waters will recede, so we cannot provide a timeline for restart at this time," the company said.
The Colonial Pipeline Company also shut down part of critical lines that transport gasoline, diesel and aviation fuel from Houston through the southeast and up the East Coast to New Jersey. The closure prevented fuel flows along a stretch from Houston to Hebert, Texas.
Colonial aims to get the affected portion of the pipeline running by Sunday after it evaluates its infrastructure.
Colonial Pipeline Gulf Coast status map
The partial closure is due to a lack of supply from idled refineries, as well as storm damage to Colonial's facilities near Lake Charles, Louisiana, according to Colonial. Fuel deliveries will be intermittent and depend on its ability to receive supplies from refineries and terminals.
"Think of Colonial Pipeline like a garden hose. It needs to have so much in there as line fill to pump and to pump normally," said Tom Kloza, global head of energy analysis at Oil Price Information Service. "Clearly, they haven't been getting the injections from Texas, so that's going to be problematic heading through next week."
Lack of product is also preventing the Explorer pipeline from transporting fuel from Houston to Tulsa, Oklahoma, and onward to Chicago, according to Lipow. However, Explorer has restarted deliveries to Dallas.
Texas City refineries were able to restart operations after Magellan Midstream Partners restarted a pipeline to the city from Houston, Lipow reported.
Kloza noted that while about 25 percent of total U.S. refining capacity is offline, something on the order of 40 percent of capacity that serves Americans east of the Rockies had been affected.
"This is an unprecedented event, and it's got some unknown outcomes," he told CNBC's "Fast Money: Halftime Report" on Thursday.
The worst-case scenario could be a price spike on the order of 40 to 60 cents that pushes gasoline prices to $2.60 to $2.75 per gallon, Kloza said.
In the Corpus Christi area, where Harvey made landfall as a Category 4 hurricane on Friday, Valero was restarting two refineries. Marathon Petroleum was also targeting a startup at its Galveston and Texas City plants on Thursday.
The startups will not be immediate because refiners follow a gradual, step-by-step process when they resume operations, explained Jack Gerard, president and CEO of the industry group American Petroleum Institute.
"These are large, sophisticated high-tech complexes, and so they do it in phases, if you will. As they graduate from one phase to the next, it typically takes a few days to do so," he told CNBC's "Squawk Box" on Thursday.