Emergency managers in the islands declared on Monday "the Keys are not open for business" and warned that there was no fuel, electricity, running water or cell service and that supplies were low and anxiety high.
As Irma's hurricane-force winds started to whip the Florida Keys, the storm stayed at a weakened 120 miles per hour (190 kph) and took slow aim at Florida.
Irma passed over Barbuda early on Wednesday as a Category 5 hurricane.
Florida Governor Rick Scott said it was going to take some time before people could return to their homes.
The storm's impact was widespread.
He said the curfew will be indefinite or until a neighborhood is deemed safe from downed power lines, overturned trees and storm debris.
In Riviera Beach, on Florida's east coast, winds partially ripped roofs off two apartment buildings, forcing rescuers to evacuate about 50 people from the complex, according to CNN. The storms eye was north of Tampa at 5 a.m. Forecasters expect it to stay inland over Florida as it heads into Georgia, before moving on to Alabama and Tennessee.
"This is a life-threatening situation".
If all those households do lose power, then it could be the largest number of outages any utility company has ever had to grapple with, FPL spokesman Chris McGrath told reporters.
President Trump's Cabinet met at Camp David on Saturday to discuss federal preparations for Irma.
With about 3 million people, the Tampa Bay metropolitan area is the second-most populous in the state. Irma is draped over Northern Georgia and Alabama, with bands stretching into SC.
A flash flood warning is in effect along the southern coast of SC, where more than 40,000 were ordered to evacuate barrier islands.
State government offices as well as some schools in Georgia will be closed both Monday and Tuesday.