The storm produced 150mm of rain in six hours over Baracoa, causing floods and cutting off roads at the already water-logged eastern tip of Cuba.
Thousands of people were evacuated, but no casualties were reported in Cuba, which has one of the most effective civil protection operations in the region.
The 14th named storm of the 2007 Atlantic storm season was not expected to strengthen into a hurricane over water, US National Hurricane Centre forecasters said on Wednesday.
Forecasters projected the storm's would veer northeast over the Bahamas on Thursday, away from Florida and clear of oil industry installations in the Gulf of Mexico.
The toll in Dominican Republic and Haiti was expected to climb once emergency workers reached communities cut off by raging rivers. Several bridges have collapsed and mudslides have blocked roads.
Thousands of people were thought to have lost their homes.
Emigdio Sosa, director of the presidential office's social assistance plan, said that 145,000 families had been given emergency aid in the form of food, blankets, mattresses and mosquito nets.
The government expects to distribute construction materials such as zinc and wood.
"We project that we will be helping more than 300,000 families," Sosa
said in a statement.
Haiti is the country most vulnerable to flashfloods and mudslides in the Caribbean because most of its trees have been felled to make charcoal.
|At least 50 people have been killed in the |
Dominican Republic and Haiti [AFP]
Eighteen bodies were counted by the national civil protection office, said Alta Jean-Baptiste, its director.
Two people died in the town of Terre Neuve. One was a 10-year-old boy swept away by floods, the other a 36-year-old woman crushed by a tree, according to Faustin Joseph, a regional civil protection official.
About 3,400 people were in emergency shelters and about 400 houses had been destroyed.
In Jamaica, one person died when a house collapsed in the rain, the disaster preparedness agency said.
Eye of the storm
The eye of the storm was about 280km south-southwest of Nassau in the Bahamas by 11am EDT (15 GMT), the hurricane centre said.
Noel was moving to the north-northwest at about 13kph with 85kph winds, the Miami-based centre said.
Thousands of people have been left without power and reservoirs in eastern Cuba have overflowed.
Strong winds, caused by the storm's interaction with a high pressure zone over the southeastern US, sent waves crashing on to southeast Florida's Atlantic beaches and rain whipping down the streets of Miami.