Prime Minister Roosevelt Skerrit said Thursday on social media that people were missing after floods wiped out roads and swamped villages.
"Our primary concern at the moment is for the preservation of life in Dominica," he wrote. "We are now going to be focused on a search-and-rescue mission. We will focus on infrastructure after."
The Caribbean Disaster Emergency Management Agency said 25 to 30 people were missing.
As of 8 p.m. ET, the center of Erika had moved west-northwest, and Dominica was getting some relief from the downpours.
Still there was a tropical storm warning that included islands from Puerto Rico to the Bahamas.
Erika was expected to produce rainfall of 4 to 8 inches -- with a maximum of 12 inches possible -- across parts of the Leeward Islands (which include Dominica), the Virgin Islands, Puerto Rico, the Dominican Republic, the Turks and Caicos Islands, and the southeast Bahamas through Saturday.
"These rains could cause life-threatening flash floods and mudslides," the hurricane center said.
Erika's maximum sustained winds were 45 mph, with higher gusts, the forecasting center said. Tropical storm force winds extended outward up to 140 miles from the center, it said.
The storm is expected to pass the Virgin Islands and Puerto Rico on Thursday night.
, the chief executive officer of Dreamy Weddings & Tours Inc., said her staff and friends in Dominica "aren't doing so well. Erika has wreaked havoc there."
An employee on Dominica told her that a friend's family was missing after their house was swept away.
John, who lives in St. Kitts, posted several images sent to her from Dominica on Twitter that show the fast-flowing water. In one, the muddy water fills the street and spills over into yards.
There was also extensive damage at the country's airports. A photo on the Prime Minister's Facebook page
showed a small plane with water up to the doors.
John wrote in an email that the sky was very gray in St. Kitts and the rain has been constant since it began Wednesday night. Though this isn't the busiest time of year for island weddings, Erika still was threatening events planned this week, John said.
Erika's winds, light for a tropical storm, should not get much worse anytime soon.
"No significant change in strength is anticipated during the next 48 hours," the hurricane center said.
That doesn't mean Erika -- the fifth named storm of the Atlantic hurricane season -- will sputter out.
By the end of the week, forecast models predict that the storm will intensify. Erika is expected to reach hurricane status with 75 mph sustained winds as it approaches South Florida on Monday.
The five-day graphical forecast shows the storm taking a path up the east coast of the Sunshine State and remaining a hurricane through Tuesday.