The most powerful storm to hit the Caribbean islands of the Bahamas since records began has torn roofs from buildings and caused severe flooding.
Hurricane Dorian, a category five storm, has sustained winds of up to 180mph (285km/h).
A "life-threatening" storm surge of 23ft (7m) is also predicted in places, officials warn.
The hurricane is moving slowly westwards and may hit areas of the eastern US seaboard.
The US states of Florida, Georgia, North and South Carolina have all declared states of emergency.
Areas of the Abaco islands were under water after the storm hit the Bahamas' Elbow Cay soon after midday (16:00 GMT) on Sunday.
The storm also battered Grand Bahama island with high winds and torrential rainfall.
Bahamas residents posted footage showing floodwaters engulfing some homes after high winds had torn their roofs off. Videos also show capsized boats floating in floodwaters filled with debris.
There are also reports of power cuts and limited access to internet around the country's 700 islands.
The government has opened 14 shelters and names dozens of churches, schools and other buildings on its official lists of emergency shelters.
But as sites become full, there is concern that people will be forced to take refuge in other places that aren't listed to receive food and water from the government.
Louby Georges, director of international affairs for Human Rights Bahamas, told the New York Times that some residents were becoming desperate.
"People are sending voice notes, people are crying," he said. "You can hear people hollering in the background."
Officials have also expressed dismay over some residents choosing to ignore evacuation orders.
"The end could be fatal," said Samuel Butler, assistant police commissioner. "We ask you, we beg you, we plead with you to get to a place of safety."
Dorian is expected to continue to move over Grand Bahama Island on Monday.
It is then due to move closer to Florida's east coast late on Monday and through to Tuesday night local time.
Hurricanes, which vary in strength from category one to five on the Saffir-Simpson scale, tend to get stronger as they move over warm waters like those off the coast of Florida.
Dorian has also grown larger in size, with hurricane-force winds extending up to 45 miles (75km) from the storm's centre.
Prime Minister Hubert Minnis announced an evacuation order for parts of Grand Bahama and the Abaco Islands, both in the north of the archipelago. All tourists were asked to leave those areas.
Mr Minnis was visibly upset as he addressed a news conference on Sunday.
"This is probably the most sad and worst day of my life," he said, calling Dorian a "monster storm".
"We're facing a hurricane... one that we've never seen in the history of the Bahamas," the prime minister added.
President Donald Trump has cancelled a planned trip to Poland and met emergency management officials.
He told reporters on Sunday that the storm "looks monstrous" and the US east coast "will be ultimately impacted and some of it very, very severely".
President Trump has also issued a federal state of emergency for Florida, and the state's governor, Ron DeSantis, has activated 2,000 National Guard troops, with another 2,000 on standby.
Evacuation orders have been given in coastal areas of Florida and South Carolina.
As Dorian crawled towards the US, shoppers were seen queuing to buy supplies such as medication and fuel.
Popular attractions, including Disney World in Orlando, have said they are "closely monitoring" the storm. The coastal city of Miami has also ordered the removal of electric rental scooters from the streets to avoid them becoming projectiles.