Hurricane Michael is expected to strengthen rapidly over the next 24 to 36 hours and will be "a unsafe major hurricane when it reaches the northeastern Gulf Coast on Wednesday", the National Hurricane Center says.
State offices, schools and universities were to close on Tuesday through the end of the week in panhandle counties.
Leslie is around 1,090 miles west of the Azores, an archipelago composed of nine volcanic islands in the North Atlantic, with maximum sustained winds of 60mph.
Florida's governor has mobilised National Guard troops and ordered Gulf Coast residents to head inland as Hurricane Michael churned toward shore, with the storm forecast to strengthen rapidly before making landfall on Wednesday.
In a Facebook post Monday, the Wakulla County Sheriff's Office said no shelters would be open in Wakulla County because Michael was forecast to become a major hurricane with winds topping 111 miles per hour (178 kph).
The center reported that the hurricane was likely to produce potentially catastrophic wind damage where its core moves ashore, and risky hurricane-force winds will extend well inland across portions of the Florida Panhandle, southern Georgia, and southeast Alabama as Michael moves inland.
Florida Gov. Rick Scott says Hurricane Michael is a "monstrous storm" that has the potential to be devastating to the Florida Panhandle.
Heavy rainfall was projected for areas in the storm's path.
"Hurricane Michael is forecast to become a major hurricane and it will produce wide-spread power outages and debris that will challenge our response and recovery in the southern and Wiregrass counties".
"We are already seeing the impacts of Michael here in Central Florida with on and off rain throughout the day", Bridges said. In a press conference on Monday, he said Hurricane Michael was a "massive storm".
"I haven't made up my mind yet, but I know some of my staff are going", said Dave Trepanier, owner of Firefly, a restaurant a block from the beach in Panama City, Bay County, an area where the hurricane is expected to come ashore. Some parts of Alabama are under tropical storm watches or warnings.
Michael was a Category 1 hurricane but could make landfall as a Category 3, and forecasters warned it could send down 10 to 30 centimetres of rain.
Chatham Emergency Management Agency has entered OPCON 4 and is monitoring Tropical Storm Michael.
Another national, Neil Fung, said the storm looks like " a major one". A storm surge warning was issued for Florida's Gulf coast from the Okaloosa-Walton County Line to Anclote River.
Tropical Storm Michael became a named storm on Sunday.