Hurricane Matthew slammed into Haiti's southwestern tip with howling 145 mph winds Tuesday, knocking down trees and tearing off roofs in the poor and largely rural area, while inundating neighborhoods in floodwaters and mud.

By nightfall, at least 11 deaths had been blamed on the powerful storm during its week-long march across the Caribbean. But with a key bridge washed out, impassable roads and phone communication cut off with Haiti's hardest-hit area, there was no way to know how many people might be dead or injured.

Matthew, slightly weakened but still a dangerous Category 4 storm with 130 mph winds, whipped at Cuba's sparsely populated eastern tip Tuesday night, as it headed for a two-day run up the length of the Bahamas that would take it near the U.S. coast.

Twenty-foot waves pounded the seafront promenade in the Cuban town of Baracoa. Powerful winds rattled the walls of homes and heavy rain caused some flooding. But state media said late Tuesday there were no immediate reports of serious damage.

Hours after Matthew made landfall on Haiti's now-marooned southwestern peninsula, government leaders said they couldn't fully gauge the impact.

"What we know is that many, many houses have been damaged. Some lost rooftops and they'll have to be replaced while others were totally destroyed," Interior Minister Francois Anick Joseph said.

At least five deaths were blamed on the storm in Haiti, including a 26-year-old man who drowned trying to rescue a child who fell into a rushing river, authorities said. The child was saved. The mayor in flooded Petit Goave reported two people died there, including a woman who was killed by a falling electrical pole.

Four deaths were recorded in the neighboring Dominican Republic and one each in Colombia and in St. Vincent and the Grenadines.

Forecasters said Matthew could be threatening Florida by Thursday night and would likely push its way up the East Coast through the weekend. The forecast triggered a rush by Americans to stock up on food, gasoline and other emergency supplies.

The storm -- at one point the most powerful hurricane in the region in nearly a decade -- blew ashore around dawn in the poorest country in the Western Hemisphere, hitting a corner of Haiti where many people live in shacks of wood or concrete blocks.

Mourad Wahba, U.N. secretary-general's deputy special representative for Haiti, said at least 10,000 people were in shelters and hospitals were overflowing and running short of water. Wahba's statement called the hurricane's destruction the "largest humanitarian event" in Haiti since the devastating earthquake of January 2010.

Matthew left the peninsula that runs along the southern coast of Haiti cut off from the rest of the country. A bridge in the flooded town of Petit Goave was destroyed, preventing any road travel to the hard-hit southwest. Local radio said water was shoulder high in parts of the city of Les Cayes.

Milriste Nelson, a 65-year-old farmer in the town of Leogane, said his neighbors fled when the wind ripped the corrugated metal roof from their home. His own small yard was strewn with the fruit he depends on for his livelihood.

"All the banana trees, all the mangos, everything is gone," Nelson said as he boiled breadfruit over a charcoal fire in the gray morning light. "This country is going to fall deeper into misery."

Haitian authorities had tried to evacuate people from the most vulnerable areas ahead of the storm, but many were reluctant to leave their homes. Some sought shelter only after the worst was already upon them.

Before cellular communications went out in the southwestern town of Jeremie, one resident described seeing panicked people who didn't evacuate coastal homes and were frantically seeking shelter at dawn.

"Some people who lived by the sea are walking with their things through flooded streets looking for somewhere to go," said Iralien St. Louis, a photographer who was hunkered down at his home.

Matthew was expected to drop 15 to 25 inches of rain, and up to 40 inches (100 centimeters) in isolated places of Haiti, along with up to 10 feet (3 meters) of storm surge and battering waves.

"They are getting everything a major hurricane can throw at them," said Dennis Feltgen, a meteorologist with the U.S. National Hurricane Center in Miami.

Matthew briefly reached the top classification, Category 5, as it moved across the Caribbean late last week, becoming the strongest hurricane in the region since Felix in 2007.

As of 11 p.m. EDT (0300 GMT), the storm's center was moving back into open waters from Cuba's northeastern coast. It was heading north at 8 mph (13 kph). Its sustained winds were 130 mph (215 kph).

In the U.S., Florida Gov. Rick Scott urged coastal residents to prepare for the possibility of a direct hit and line up three days' worth of food, water and medicine. The Red Cross put out a call for volunteers in South Carolina. And the White House said relief supplies were being moved to emergency staging areas in the Southeast.

People raced to supermarkets, gas stations and hardware stores, buying up groceries, water, plywood, tarps, batteries and propane. South Carolina Gov. Nikki Haley said she would issue an evacuation order Wednesday so 1 million people would have time to leave the coast.

In the storm-hardened Bahamas, Prime Minister Perry Christie voiced concern about the looming hurricane. "We're worried because we do not control nature," he said.