The northern Abaco Islands have been hit the hardest by the category 4 hurricane.
The prime minister did not give further details on the victims, adding that the Bahamas were in the midst of a "historic tragedy."
Minnis urged residents to stay indoors and said the government's focus was now on search and rescue operations.
The hurricane is expected to travel northwest and hit the US southern state of Florida on Tuesday. The United States has declared a state of emergency in four states along the country's southeast coast. Florida's St. Johns County has issued a mandatory evacuation order.