It's the 24th storm in a record-breaking Atlantic season.
There have been floods and landslides in Honduras and Belize is on alert.
Forecasters believe Gamma will swing north-east, away from Mexico's Yucatan peninsula, which was battered by Hurricane Wilma a month ago.
The storm is expected to hit Florida early next week.
The US states has been hit by eight hurricanes and three tropical storms in the past year.