The National Hurricane Center said Tropical Storm Ian had formed over the central Caribbean Sea Friday night.
The NHC said hurricane conditions could impact the Cayman Islands by Monday.
A hurricane watch is in effect for the Cayman Islands along with a tropical storm watch for Jamaica.
"Intensification is expected to be gradual during the next 36 hours while Ian gets better organized in a lower-shear environment, but after that time, conditions will be conducive for faster strengthening," hurricane forecasters added.
The official forecast from the NHC shows Ian as a major category 3 hurricane by Monday with maximum winds of 115 miles per hour as it approaches Florida, though the agency warns the system could be stronger than forecast.
For now, there is no immediate threat to Louisiana from Ian.