Meteorologists say the storm known as Rita has strengthened into a category 1 hurricane.
The U.S. National Hurricane Center says Rita is packing winds of about 120 kilometers per hour as it moves west, past the Bahamas and toward the Florida Keys.
The storm reportedly caused little damage in the Bahamas. However, thousands of tourists and residents have fled the Keys, a low-lying chain of islands off Florida's southern coast.
Hurricane warnings remain in effect for the Keys and parts of western Cuba, including Havana.
Forecasters expect Rita to enter the Gulf of Mexico by Wednesday, and say it is possible that Rita will strike areas along the U.S. Gulf Coast devastated three weeks ago by Hurricane Katrina.