The storm weakened as it moved up the state's western coast overnight but Miami and other urban areas have been battered and flooded.
Six million homes - 62% of the entire state - are without power. In the islands of the Florida Keys, officials have warned of a "humanitarian crisis".
Media reports link at least four deaths to the storm.
Irma, which hit Florida as a category four hurricane on Sunday, has now been downgraded to a tropical storm.
It cut a devastating track across Caribbean islands, killing at least 37 people there.
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Florida Governor Rick Scott said it was "going to take some time" before people could return to their homes, the Miami Herald website reports.
Speaking as he went on an aerial tour of the Keys to survey the damage early on Monday, he said: "Power lines are down throughout the state. We've got roads that are impassable, so everybody's got to be patient as we work through this."
All eyes on the Keys
Miami dodged a bullet by and large. The eye of the storm did not hit the city but it did wallop the Florida Keys, of course, and that is where the concern is now.
Communications were pretty bad even on Friday. A number of people who had fled the Keys and checked into our hotel were struggling to keep in touch with relatives who had decided to stay behind.
Reports say that 10,000 people decided to ride out the storm. We do not know what state they are in now.
The first job rescue services will have to do is to test the integrity of the 42 bridges linking the Keys. If one of those is down, it could cause problems because it could strand any one of the islands.
The entire Keys are closed. There is no way of getting in there at the moment while the authorities assess the damage.
How big will the disaster response be?
Power lines came down in 80% of Miami alone and large areas of the city were flooded, although the city appears to have escaped lightly compared to other parts.
Drone footage from Naples, a town on the coast of the Gulf of Mexico about 125 miles (200km) to the north-west, shows rows of shattered suburban homes on streets under water.
President Donald Trump has approved a major disaster declaration and emergency federal aid for Florida, describing the hurricane as a "big monster".
Funds will be needed to care for victims, clean up debris, restore power, and repair damage to homes and businesses.
Martin Senterfitt, emergency management director for Monroe County (population 73,000), said a huge airborne relief mission mounted by the Air Force and Air National Guard was in the works, the Miami Herald reports.
"Disaster mortuary teams", he said on Sunday afternoon, would be dispatched to the Keys, which are part of Monroe.
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