The company is believed to have been hit by the DarkSide ransomware, a recent addition to the swarms of ransomware that attack Microsoft's Windows operating system.
Colonial is the biggest American refined products pipeline system and can carry more than three million barrels of petrol, diesel and jet fuel between the US Gulf Coast and the New York Harbour area, according to Wikipedia.
The company was founded in 1961 and construction of the pipeline began in 1962.
"While our mainlines (Lines 1, 2, 3 and 4) remain offline, some smaller lateral lines between terminals and delivery points are now operational," Colonial said.
"We are in the process of restoring service to other laterals and will bring our full system back online only when we believe it is safe to do so, and in full compliance with the approval of all federal regulations."
The operators of the DarkSide ransomware have made no mention of the attack on their website where the last listing was on 23 April.
But if the company pays whatever ransom is demanded, then there will be no listing.
Andrew Rubin, chief executive and co-founder, micro-segmentation provider Illumio, said: "This could be the most impactful ransomware attack in history, a cyber disaster turning into a real-world catastrophe.
"It's an absolute nightmare, and it's a recurring nightmare. Organisations continue to rely and invest entirely on detection as if they can stop all breaches from happening.
"But this approach misses attacks over and over again. Before the next inevitable breach, the president and Congress need to take action on our broken security model. This begins (but does not end) with the adoption of a Zero Trust strategy.
"But instead of talking about and doing the hard work we need to do, we'll watch the financial markets on Monday reward the entire security industry for failing to stop modern attacks from spreading into a disaster."
Marty Edwards, vice-president of Operational Technology Security at security firm Tenable and the longest-serving director of ICS-CERT, commented: "Cyber attacks are a real and present danger to critical infrastructure around the world and, by extension, every single consumer.
"If reports are accurate, the Colonial Pipeline incident has all of the markings of a possible ransomware attack that began in the IT environment and, out of precaution, forced the operator to shut down operations.
"Ransomware has been a favoured attack vector of cyber criminals because of its effectiveness and return-on-investment. That's precisely why bad actors have recently set their sights on critical infrastructure. Shutting down operational technology environments can cost hundreds of millions of dollars which forces providers to outweigh the costs.
"We should not under-estimate these groups. Many of them now have help-desks, technical support, payroll processing and subcontractors. They are essentially full-fledged criminal corporations operating in the digital world. While it's unknown how this attack played out, it's yet another reminder of the increasing threats to critical infrastructure we all rely on."
Ransomware expert Brett Callow, who works for the New Zealand-headquartered security outfit Emsisoft, had a sharper response. "Nero fiddled as Rome burned; governments dithered as the ransomware problem steadily worsened," he said. "Incidents such as this are the result of that dithering."