"This is not the type of storm that's going to rip off a lot of roofs or cause the type of damage we normally see in a large hurricane," said Craig Fugate, the state's emergency management chief.
At 8 p.m. EDT, Fay was about 105 miles south of Naples and moving north at about 9 mph. Sustained winds were about 60 mph with some higher gusts.
National Hurricane Center officials said the storm would likely make landfall sometime Tuesday morning. Forecasters said Fay would probably be at or near hurricane strength, which is winds of at least 74 mph.
Between 4 and 10 inches of rain is possible across mainland Florida, so flooding is a threat even far from where the center comes ashore, said Stacy Stewart, a senior hurricane specialist at the National Hurricane Center.
"This is a broad, really diffuse storm.