The Category 1 hurricane with maximum sustained winds of 90 mph (150 kph) was moving toward the west-northwest on a path that could take it over vulnerable Haiti later in the week.
The U.S. National Hurricane Center in Miami said some more weakening is forecast during the next 24 hours, and it should maintain most of its strength into Tuesday.
But Daniel Brown, a center forecaster, said Tomas was "likely to strengthen when it's over the central Caribbean" and Haiti and the Dominican Republic could be hit by rains from outer bands in another few days.
By Sunday, no deaths and few injuries were reported in a cluster of islands at the Caribbean Sea's eastern entrance. Authorities in St. Vincent and the Grenadines said two workmen were hospitalized after they were blown off a roof during the hurricane's passage.
St. Vincent Prime Minister Ralph Gonsalves said fierce winds tore roofs from scores of homes and more than 1,000 people sought emergency shelter as the islands plunged into darkness. Widespread flooding triggered landslides that cut off as many as 30 roads, marooning hundreds of residents.
"I have been told that over 300 houses have suffered some level of damage," Gonsalves said Sunday morning. "There is also serious damage to fruit trees, bananas, and other infrastructure and this is going to cost the state millions."
Chief Agricultural Officer Reuben Robertson said "most of our farmers have taken a serious beating."
On the nearby island of St. Lucia, high winds tore off the roofs of a hospital, a school and a stadium and toppled a large concrete cross from the roof of a century-old church, government officials said. Heavy rains caused a landslide that blocked a main highway linking the capital to the island's southern region.
At least 20,000 people were without power on Martinique, and streets flooded and tree branches were down. A cruise ship carrying nearly 2,000 tourists docked instead in Dominica.
Tomas earlier toppled power lines and damaged houses in Barbados as a tropical storm.
Forecasts said the Atlantic season's 12th hurricane could drop up to 6 inches (15 centimeters) of rain in the region. Rain was still drenching the eastern Caribbean islands on Sunday.
It was forecast to head toward Haiti, which is struggling to recover from a devastating Jan. 12 earthquake and to cope with a deadly cholera outbreak.
Haitian authorities warned southern and western regions - including the quake-ravaged capital of Port-au-Prince, where an estimated 1.3 million people are living in tent camps - to be on guard for high winds, thunderstorms and possible flooding.
But with few usable storm shelters and no feasible evacuation plan, residents will largely be on their own.
Associated Press writers Guy Ellis in Castries, St. Lucia, and Rodolphe Lamy in Fort-de-France, Martinique, contributed to this report.