Leaving Haiti in "total disaster," Hurricane Matthew slammed into Cuba Tuesday night.

Hit in some areas by 24-foot waves, Cuba faced high winds, strong storm surge and torrential downpours as the storm marched across the country.

According to AP, the storm destroyed dozens of homes in Cuba's easternmost city, Baracoa, and left hundreds of others damaged.

Tweets coming out of Baracoa seem to indicate extensive damage in the area from extreme wind and storm surge.

Apart from Baracoa, there were no other reports of extensive damage, the AP reports. However, a large shipping container was washed three blocks inland from storm surge.

At least 11 deaths have been attributed to the storm. Five deaths were reported 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. Two people died in Petit Goave, including a woman who was by a falling electrical pole, reported the mayor of the town, according to the Associated Press.

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

Haiti Libre reported on Wednesday that one person remains missing and dozens have been injured.

'Total Disaster' in Haiti

"It's the worst hurricane that I've seen during my life," Fidele Nicolas, a civil protection official in Nippes, told AP. "It destroyed schools, roads, other structures."

According to Haiti Libre, 14,530 people have been displaced , 2,703 families are affected and 1,885 houses are flooded.

After a request for aid from Haiti, the United States deployed the U.S.S.George Washington carrier and the amphibious transport dock Mesa Verde, supported by Navy and Marine aviation, to provide relief to the ravaged country after the storm, along with the hospital ship Comfort, according to ABC 13.

Tuesday evening, President de facto Jocelerme Privert said he and other government officials would be traveling to southwest Haiti to assess the damage.

"Tomorrow morning (Wednesday) as soon as weather permits it and the roads are re-opened the Government, ministers, the Prime Minister, the President, everyone in the State will travel around all the places in the country that are disaster to assess the damage, to provide answers that the circumstances require," Privert said.

Major flooding was reported in several southern towns, including Petit Goave, where the Ladigue Bridge collapsed Tuesday, isolating southwest Haiti from the rest of the country, reports Haiti Libre.

"The river has overflowed all around us," church pastor Louis St. Germain told CNN. "It's terrible... a total disaster."

"It's much too early to know how bad things are but we do know there are a lot of houses that have been destroyed or damaged in the south," Jean-Baptiste told the AP.

(MORE: Track Hurricane Matthew )

Much of the local population were forced from their homes and at least 10,000 people were in shelters and hospitals, U.N. secretary-general's deputy special representative for Haiti Mourad Wahba told AP. The refuge facilities became crowded and began running short of water. The roof was blown off the hospital in the city of Les Cayes.

Wahba called the hurricane's destruction the "largest humanitarian event" in Haiti since the devastating earthquake of January 2010.

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 Tuesday , reports CNN.

"We have already recorded a landslide between Les Cayes and Tiburon in Haiti's Sud department," director of civil protection Marie-Alta Jean-Baptise told AFP.

(MORE: Southeastern U.S. Prepares for Possible Matthew Impacts )

In Les Cayes and the Valley of Jacmel, several homes lost roofs , Haiti Libre reports. In Nippes, dozens of homes were severely damaged and others were swept away by raging flood waters.

Haitian Sen. Nenel Cassy told the Miami Herald "the situation in the Nippes [region] is truly catastrophic ."

"The amount of rain we're seeing accumulate is enormous," the assistant director of the aid organization CARE in Haiti, Laura Sewell, told NPR Tuesday morning. Speaking from Port-au-Prince, she said she had heard informal reports of mudslides elsewhere in the country.

"What we're looking at here is a lot of flooding," said Sewell. "Haiti is very mountainous so there's a good chance of landslides and mudslides."

(MORE: How You Can Help the Victims in Haiti )

Local radio reported that the water was shoulder high in parts of Les Cayes, near where Matthew came ashore, according to AP.

As the storm made landfall, residents previously reluctant to evacuate to shelters flooded them on Tuesday, bringing the total number of evacuees in shelters to nearly 10,000 people.

Homes Destroyed in Cuba

The hurricanerolled across the sparsely populated tip of Cuba overnight, destroying dozens of homes in Cuba's easternmost city, Baracoa, and leaving hundreds of others damaged, the AP reported.

The road joining Guantanamo's municipalities of Imías and Baracoa became flooded and impassable , according to Diario Las Américas.

Some 316,000 people were evacuated from the east of the island. According to the Pentagon, 700 family members were evacuated from the Guantanamo Bay naval base to Florida.

MORE ON WEATHER.COM: Hurricane Matthew - October 2016