MIAMI—Authorities on Thursday ordered more than 650,000 people to evacuate the Miami area as Hurricane Irma churned toward a possible collision with the mainland U.S. and killed at least 11 people in the Caribbean.

“These are areas that may experience life-threatening storm surge,” said Carlos Gimenez, mayor of Miami-Dade County. “I cannot stress this enough: don’t wait to evacuate.”

Irma—one of the most powerful storms ever recorded over the Atlantic—weakened to a Category 4 storm early Friday, according to the National Hurricane Center.

The storm was heading through the southeastern Bahamas on Friday with maximum-sustained winds of 155 miles an hour, after battering the Turks and Caicos Islands. The current forecast track calls for the storm to approach south Florida on Saturday, with Miami squarely in its potential track.

Hurricane and storm-surge warnings were officially issued for south Florida including the Florida Keys. Gov. Rick Scott on Thursday expressed worry about the breadth of the storm and flooding potential as he implored residents to heed evacuation orders.

“Look at the size of this storm, it’s huge. It’s wider than our entire state and could cause major and life-threatening impacts on both coasts,” Mr. Scott said Thursday.

The National Hurricane Center forecast the storm surge in parts of south Florida could reach 5 to 10 feet above ground, if the peak surge coincides with high tide. “We could see houses covered,” Mr. Scott said.

Hurricane Irma's Rampage

Miami-Dade County’s Mr. Gimenez said officials are preparing shelters to accommodate as many as 100,000 people. He urged residents to stay with friends who live in safe areas in the county, rather than drive away.

“Look, if 600,000 people decide they want to leave Miami-Dade tomorrow, that’s going to be a mess,” he said. “We need our neighbors and co-workers, et cetera, to take some folks in.”

Evacuees were clogging highways and backing up traffic on Thursday amid worries about gasoline shortages in the state.

Gina Sneiderman sat in bumper-to-bumper traffic on I-75 somewhere between Ocala, Fla., and the Georgia state line, recounting the fear she had when Hurricane Wilma rattled her house in Boca Raton back in 2005, causing significant damage.

Looking at Irma, Ms. Sneiderman and her husband, Mike, decided to get out of town. They secured the house and packed up a week’s worth of clothes, five cases of water and important papers, like insurance policies, and began heading north on the Florida Turnpike.

“This storm is crazy and we weren’t going to risk it,” she said.

But traffic was tough, with long lines of vehicles backed up. At one toll crossing, Ms. Sneiderman said, all but two lanes had been closed, causing an 8-mile jam that took about an hour to clear.

Florida Governor Rick Scott gives an update regarding Hurricane Irma on Wednesday in Doral, Fla. Photo: Mark Wilson/Getty Images

“We’re now in bumper-to-bumper traffic between 10 and 15 miles an hour,” she said.

Briana Beaty of North Palm Beach won’t have to contend with highway congestion when she and family members leave South Florida on Friday.

A private plane offered by a family friend will ferry her and her three daughters ages 1, 3 and 6, along with their nanny and her mother-in-law, to a resort in the north Georgia mountains where she said she booked the last three rooms.

Her husband, who owns 30 rental properties in the area, will stay behind in their 3-year-old home, satellite phone at the ready, she said.

Ms. Beaty, 36, said she might have considered staying put if not for the children. “I just don’t think it’s an option with little babies and the potential to not have water and power for a while,” she said.

Irma also poses a rising threat to other states in the Southeast, with forecasts predicting the storm could potentially reach the Carolinas by early next week. The governors of Georgia, South Carolina and North Carolina declared states of emergency for all or part of their states on Wednesday.

Hurricane Irma tore through Tortola and the rest of the British Virgin Islands on Thursday, leaving much of the area destroyed and thousands homeless. Video/Photo: AP

Georgia Gov. Nathan Deal on Thursday ordered a mandatory evacuation for all areas east of Interstate 95 starting Saturday, including Savannah, home to about 147,000 people. In South Carolina, Gov. Henry McMaster said he may issue a mandatory evacuation order effective Saturday morning, and that there would be lane reversals on I-26 that runs north from Charleston.

Mr. McMaster also ordered the evacuation of health-care facilities including hospitals and nursing homes in certain coastal counties.

He warned there could be a burden on South Carolina highways because of residents fleeing Florida and Georgia, and I-95 was already congested on Thursday as people drive north. “If you can leave now, go ahead,” the governor said.

Puerto Rico, with a population of about 3.4 million, appeared to have been spared the ferocious assault that Irma delivered to other Caribbean islands, but the extent of damage remained unclear and the U.S. territory was contending with widespread power outages and the threat of continued flooding. A woman died in Arecibo, on the northern coast, after she fell while walking to an emergency shelter, according to Ernesto Morales, a National Weather Service meteorologist in San Juan.

Gov. Ricardo Rosselló on Thursday said 68% of the customers of Puerto Rico’s electric utility lacked power, with outages affecting hospitals, forcing many to rely on generators and requiring the relocation of some patients. Before Irma’s arrival, an executive with the utility company had said it could take months to restore electricity to many residents.

President Donald Trump approved on Thursday a major disaster declaration for the U.S. Virgin Islands. There are reports that 25 buildings in St. Thomas lost roofs and two shelters flooded, Mr. Morales said.

With hurricane season still at its peak, Irma isn’t the only threat on the horizon. Hurricane Jose strengthened to a Category 3 storm in the Atlantic on Thursday and triggered a hurricane watch in Antigua and Barbuda. A third storm, Hurricane Katia, is threatening Mexico.

—Erin Ailworth contributed to this article.

Write to Jon Kamp at jon.kamp@wsj.com, Scott Calvert at scott.calvert@wsj.com and Arian Campo-Flores at arian.campo-flores@wsj.com