Hurricane Matthew pounded western Haiti Tuesday morning, packing winds of 145 mph as it made landfall near Les Anglais, Haiti, according to the National Hurricane Center.
The "extremely dangerous" storm has already killed at least three people, caused cruise ships to change course and prompted officials to declare states of emergency.
And officials have warned that the death toll could climb.
"We've already seen deaths. People who were out at sea. There are people who are missing. They are people who didn't respect the alerts. They've lost their lives," Interim Haitian President Jocelerme Privert said at a news conference.
At 8 a.m. ET Monday, the Category 4 hurricane was churning north across inland Haiti at about 9 mph, the hurricane center said.
Ferocious rain and wind were already thrashing the Caribbean nation before the storm made landfall. And forecasters said Tuesday that life-threatening flash floods and mudslides were likely.
Up to 40 inches of rain could be dumped on the impoverished nation, which is still recovering from a devastating earthquake that struck six years ago and a cholera outbreak after that.
As Matthew drenched Haiti with dozens of inches of rain, Cuba, the Bahamas and the United States took steps to prepare for the storm's arrival in the coming days.
Forecasters predict the storm will move near eastern Cuba and over portions of the Bahamas later Tuesday.
Death toll rising
Three people have died in incidents connected to Hurricane Matthew within the past week, authorities said.
In Haiti, Guillaume Albert Moleon, director of communications for the Interior Ministry, said one fisherman died on Sunday. A second fisherman is presumed dead, but his body has not been recovered.
In St. Vincent and the Grenadines, a teenage boy died in a landslide as he was cleaning a drain behind his house, according to Michelle Forbes, deputy director for the National Emergency Management Office. The boy died Wednesday after storms from Matthew passed over the island.
The hurricane could cause further devastation for Haiti as much of the country's infrastructure remains weak after the 2010 earthquake that killed more than 200,000 people.
John Hasse, the humanitarian aid agency World Vision's national director in Haiti, said 400 workers were there, ready to help rural residents whose poorly constructed houses could be leveled by the storm.
"It's not safe to stay in your house," Laura Sewell, CARE's assistant country director for Haiti, told CNN. "It's not a normal rainstorm. People need to move to shelters immediately."
The Haitian government, which has urged people to find shelters, has identified about 1,000 different facilities as temporary safe havens. The number of people who have sought refuge in shelters in the southern and west parts of the country now stands at more than 6,400, Civil Protection tweeted.
After the storm clears Haiti, standing water will likely continue to plague the nation, Hasse said. Haiti continues to recover from a post-quake cholera outbreak that killed another 10,000 people.
"That means a potential spike in cholera cases," Hasse said. "Other mosquito-borne diseases that have been more or less controlled are going to rear their heads."
Collision course for Cuba
After passing through Haiti, forecasters expect Matthew to churn toward Cuba, where it is expected to move near the eastern coast Tuesday afternoon. The storm could dump up to 20 inches of rain in some isolated parts of the country.
The United States, taking no chances, began to airlift 700 family members of military personnel stationed at Guantanamo Bay to Florida this weekend. Essential military personnel and 61 detainees -- held by the United States as alleged enemy combatants -- will not be evacuated, officials added.
The US government issued a travel advisory warning Americans in Cuba to find immediate shelter if they haven't already made travel plans.
From there, Matthew is expected to take a "prolonged trip" toward the Bahamas that's expected to last through Wednesday night. It would then turn toward the US while losing some of its strength, dropping down to a Category 3 with 120 mph winds.
Multiple cruise lines have rerouted some trips to get out of Matthew's path. Royal Caribbean, Disney Cruise Line, Norwegian Princess and Carnival have rerouted trips, with more changes possible.
A Carnival cruise ship that planned to stop in the Bahamas on a six-day excursion will instead visit Cozumel, Mexico, reported the Post-Courier in Charleston, South Carolina.
CNN's Ralph Ellis, Radina Gigova, Faith Karimi, Joe Sterling, Joe Sutton, Patrick Oppmann, Salim Essaid, Michael Holmes, Lindy Royce and Eliott C. McLaughlin contributed to this report.