The lawsuit was filed in New Orleans on Thursday on behalf of a Mississippi man who worked on the rig and is one of 11 people still missing after the blast.
The suit says Shane Roshto, of Amite County, Miss., was thrown overboard in the Tuesday night explosion and is feared dead.
The rig is owned by Transocean Ltd. and was under contract to oil giant BP. Both are defendants in the lawsuit.
A Transocean spokesman did not immediately respond to a request for comment and BP wouldn't discuss the suit.
Meanwhile, a Coast Guard helicopter and rescue plane resumed the search Thursday the missing workers.
The rig continued to burn as supply vessels shot water into it try to control the flames enough to keep it from sinking.
Rescue crews have covered the 1,940-square-mile search area by air 12 times and by boat five times, Petty Officer Casey Baker said. The boats searched all night, hoping the missing workers might have been able to get to a covered lifeboat with supplies.
Families waited anxiously for hourly updates. Tracy Kleppinger, whose husband, Karl, is among the missing workers, said she is hopeful he will be found alive. "For me there is no other option," Kleppinger told CBS' "The Early Show" Thursday.
Rhonda Burkeen said her husband, crane operator Aaron Dale Burkeen, 37, was among the missing. The Burkeens have two children and live in the Sandtown community in east-central Mississippi.
Transocean Ltd. spokesman Guy Cantwell said 111 workers who made it off the Deepwater Horizon safely after Tuesday night's blast were ashore Thursday, and four others were still on a boat that operates an underwater robot. A robot will eventually be used to stop the flow of oil or gas to the rig, cutting off the fire. He said officials have not decided when that will happen.
Seventeen others hurt in the blast had been brought to shore Wednesday with burns, broken legs and smoke inhalation. Four were critically injured.
A slow trek across the water brought most of the uninjured survivors to Port Fourchon, where they were checked by doctors before being brought to a hotel in suburban New Orleans to reunite with their relatives early Thursday.
One worker said he was awakened by alarms and scrambled to get on a life boat.
"I've been working offshore 25 years and I've never seen anything like this before," said the man, who like others at the hotel declined to give his name.
Stanley Murray of Monterey, La., was reunited with his son, Chad, an electrician aboard the rig who had ended his shift just before the explosion.
"If he had been there five minutes later, he would have been burned up," Stanley Murray said.
The Deepwater Horizon is one of the largest of the 90 drilling rigs now operating in the Gulf of Mexico. At 396 feet long and 256 feet wide, it's 36 feet longer and nearly 100 feet wider than a football field, CBS News correspondent Kelly Cobiella reports.
A column of boiling black smoke rose hundreds of feet over the Gulf of Mexico. Officials said environmental damage appeared minimal so far.
Adrian Rose, vice president of Transocean, said the explosion appeared to be a blowout, in which natural gas or oil forces its way up a well pipe and smashes the equipment. But precisely what went wrong was under investigation.
A total of 126 workers were aboard. Seventy-nine were Transocean workers, six were BP employees and 41 were contracted.
Working in the oil industry is more dangerous than working in, Cobiella reports. On rigs in the Gulf of Mexico alone there have been 59 fatalities, more than 1,300 injuries and 853 fires since 2001.
The blast could be one of the nation's deadliest offshore drilling accidents of the past half-century.
One of the deadliest was in 1964, when a catamaran-type drilling barge operated by Pan American Petroleum Corp. near Eugene Island, about 80 miles off Louisiana, suffered a blowout and explosion while drilling a well. Twenty-one crew members died. The deadliest offshore drilling explosion was in 1988 about 120 miles off Aberdeen, Scotland, in which 167 men were killed.
Rose said the Deepwater Horizon crew had drilled the well to its final depth, more than 18,000 feet, and was cementing the steel casing at the time of the explosion.
"They did not have a lot of time to evacuate. This would have happened very rapidly," he said.
According to Transocean's website, the rig was built in 2001 in South Korea and is designed to operate in water up to 8,000 feet deep, drill 5½ miles down, and accommodate a crew of 130. It floats on pontoons and is moored to the sea floor by several large anchors.
Workers typically spend two weeks on the rig at a time, followed by two weeks off. Offshore oil workers typically earn $40,000 to $60,000 a year - more if they have special skills.
Working on offshore oil rigs is a dangerous job but has become safer in recent years thanks to improved training, safety systems and maintenance, said Joe Hurt, regional vice president for the International Association of Drilling Contractors.
Since 2001, there have been 69 offshore deaths, 1,349 injuries and 858 fires and explosions in the Gulf, according to the federal Minerals Management Service.