Fonie Pierre, director of Catholic Relief Services for Les Cayes, told AP: "Many people are now asking for help, but it's too late because there is no way to go evacuate them."
Nick Bryant, BBC News, Jimani border crossing, Haiti
Haiti has been taking a brutal pounding. The conditions here are atrocious - to step outside is to be drenched within seconds.
Most vulnerable have been those who inhabit the shacks along the western coastline. There, storm surges are the main danger.
People here are confronting life-threatening flooding and the likelihood of mudslides in a landscape denuded of trees.
This Category Four storm comes as this impoverished country is still recovering from the 2010 earthquake which killed more than 200,000 people, and a cholera epidemic that followed.
Many live in shanty towns that offer little protection from the high winds and rains. And many refused to evacuate, fearing that what few possessions they have left would be stolen.
The mayor of Tiburon, Remiza Denize, spoke of large waves hitting the town: "Everyone is trying to find a safe place to protect themselves."
Ms Jean-Baptiste said that there had been a major landslide between Les Cayes and Tiburon.
Guantanamo Bay evacuation
Haitian officials say that about 1,300 emergency shelters have been built, enough to accommodate 340,000 people. Both airports in Haiti are closed.
One local in Port-au-Prince said the community would unite in the face of the storm's danger.
"We are communicating amongst ourselves thanks to our own means. We will tell the people how the situation is. If things are bad then we will come together."
Unicef said more than four million children might be exposed to hurricane damage.
The UN children's fund representative in Haiti, Marc Vincent, said: "Waterborne diseases are the first threat to children in similar situations - our first priority is to make sure children have enough safe water."
An NHC statement said: "On the forecast track, the eye of Matthew will move near eastern Cuba later [on Tuesday], and move near or over portions of the south-eastern and central Bahamas [on Tuesday night] and Wednesday, and approach the north-western Bahamas on Wednesday night."
About 13,000 people were evacuated from high-risk areas in neighbouring Dominican Republic, which is also expected to get battered by rains and winds, according to the country's civil defence chief.
A hurricane alert is in place for six eastern Cuban provinces and residents are being moved from low-lying areas.
Some 700 spouses and children of US service members have been flown out of the Guantanamo Bay base, which is just 80km from where the storm could make landfall.
It is also predicted to hit the US east coast later in the week. Florida and parts of North Carolina have declared states of emergency.
Hurricane Matthew is the region's most powerful since Felix in 2007.
Hurricane scales
Category one: sustained winds of 74-95mph (119-153 km/h); some damage and power cuts
Category two: winds of 96-110mph (154-177 km/h); extensive damage
Category three: winds of 111-129mph (178-208 km/h); well-built homes suffer major damage
Category four: winds of 130-156mph (209-251 km/h); severe damage to well-built homes, most trees snapped or uprooted
Category five: winds of 157 mph (252 km/h) or higher; high percentage of homes destroyed, area uninhabitable for weeks or months