Most of them have taken shelter with friends and relatives.
More than 4,000 homes have been flooded and at least 50 totally destroyed after heavy rainfall caused rivers to break their banks.
President Danilo Medina has extended the state of emergency from four to eight provinces in the Caribbean nation.
The military rescued 13 people who were left stranded in Los Naranjos, in the north-east of the country.
Forecasters say heavy rain is expected to continue on Tuesday, although the weather front is expected to move away from the worst affected area later in the day.
More rains are expected for the weekend.
People living along rivers or on hillsides have been told to be extra vigilant and beware of flash floods and landslides.
The flooding comes less than two months after Hurricane Matthew swept over the island of Hispaniola, which the Dominican Republic and Haiti share.
Floods in the Dominican Republic have displaced more than 20,000 people, officials say.