Several communities across the country were reportedly cut off by flooded rivers as bridges collapsed in several areas.
In some areas downpours of up to 76cm were possible, the US National Hurricane Centre said.
The storm also caused authorities to shut down the international airport in the capital, Santo Domingo.
Forecasters now say the storm is expected to head towards the eastern tip of Cuba before crossing the Bahamas.
Noel is the 14th named storm of the 2006 hurricane season, which runs until the end of November.
Although that number is considered above normal, it is well below the record-breaking 2005 season when 28 storms formed, including the deadly Hurricane Katrina.