Residents of Santo Domingo suburbs bordering the swollen Ozama and Isabela rivers used mops and buckets to remove water from their homes.
Cuba's meteorology institute said on Thursday afternoon the depression was advancing in a northwest direction just off the island's northeast coast with maximum sustained winds of 55km (34 miles). More rain and storm surges are forecast for the eastern and central regions of Cuba, it said.
Cuba and the eastern Bahamas could expect 1-3 inches (2.5-7.6cm) of rainfall, the National Hurricane Center (NHC) in Miami said in its 1700 ET forecast.
Fred is expected to move along or just north of eastern and central Cuba tonight and Friday, regaining tropical storm strength as it nears the Florida Keys and southern Florida on Saturday, the NHC said.
There, it would dump 3 to 6 inches of rain, with isolated maximum totals of 8 inches.
Fred is the first named storm in a month in the Atlantic. In early July, Hurricane Elsa killed at least three people and damaged infrastructure and agriculture in Caribbean island nations east of Cuba.