The government's National Emergency Management Organization says that one of those who died is an 18-year-old college student. One man is reported missing.
Dozens of homes and at least two hotels have been evacuated because of flooding. Several roads have been closed by mudslides. Most of the damage has been just outside the capital, Roseau.
The storm came as the small island was crowded with holiday tourists. There has also been extensive flooding and landslides on the nearby island of St. Lucia, where police say a man died when a wall fell on him.