The huge storm weakened as it moved up the state's western coast overnight but Miami and other urban areas have been battered and inundated.
In the islands of the Florida Keys, the local emergency manager has warned of a looming "humanitarian crisis".
Media reports link at least four deaths to the storm.
Irma is now a category one hurricane but still has maximum sustained winds of 75mph (120km/h).
It cut a devastating track across 10 Caribbean countries and territories, killing at least 28 people there.
How big will the disaster response be?
More than 3.4 million homes in Florida are without power. 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.
The focus will be on the Keys, where as many as 10,000 people decided to ride out the storm, the BBC's Jane O'Brien reports from Miami.
The first task of the emergency services, she says, will be to check the condition of the 42 bridges linking the islands.
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.
Florida Director of Emergency Management Bryan Koon told reporters the actual physical and human damage could not be ascertained before operations began.
"We will work on those at first light [07:05 local time, 11:05 GMT],'' he said. "I don't have any numbers on fatalities at this point."
Florida Governor Rick Scott continued to tweet storm warnings early on Monday. "As little as six inches [15cm] of moving water can knock you down," he said in one message. "Stay inside. Stay safe."
Where is the storm now?
At 09:00 GMT, the centre of the hurricane was about 60 miles (100km) north of Tampa, the National Hurricane Center (NHC) said.
Some three million people live in the Tampa Bay area. The region has not been hit by a major hurricane since 1921.
Irma is expected to weaken into a tropical storm over far northern Florida or southern Georgia later on Monday but first its centre will continue to move over the western Florida peninsula, the NHC said.
Storm surge warnings are in effect for:
- The South Santee river southward to Jupiter Inlet
- Cape Sable northward to the Ochlockonee river
- Tampa Bay
Irma made landfall on Marco Island off Florida's west coast at 15:35 local time (19:35 GMT) on Sunday, with winds of up to 120mph.
How have residents felt the impact?
"We feel the building swaying all the time," restaurant owner Deme Lomas told Reuters news agency by phone from his 35th-floor apartment in Miami. "It's like being on a ship."
At least four deaths have been connected to the storm:
- A police officer working at a hurricane shelter in Hardee County was killed driving home when she collided with another vehicle being driven by a fellow officer, who also died
- A person died in a single-car crash in Orange County
- A man died in Marathon, Monroe County, on Saturday when his truck hit a tree, the sheriff's office said, adding that it was unknown if the crash had been weather-related or not
Some 6.3 million people in the state were told to evacuate before Irma arrived.
There is major disruption to transport, with Fort Lauderdale-Hollywood International Airport and Miami International Airport closed for Monday.
Amid fears of debris and reports of looting, curfews have been imposed in areas such as Miami-Dade County.
Which areas were hit before Florida?
Irma is the most powerful Atlantic storm in a decade, and has already caused widespread destruction on several Caribbean islands:
- Cuba: Officials have talked of "significant damage", without giving further details, but no casualties have been reported. Electricity is out across the capital, Havana
- St Martin and St Barthelemy: Six out of 10 homes on St Martin, an island shared between France and the Netherlands, are now uninhabitable, French officials say. They said nine people had died and seven were missing in the French territories, while four are known to have died in Dutch Sint Maarten
- Turks and Caicos Islands: Widespread damage, although extent unclear
- Barbuda: The small island is said to be "barely habitable", with 95% of the buildings damaged. Antigua and Barbuda Prime Minister Gaston Browne estimates reconstruction will cost $100m (£80m). One death has been confirmed
- Anguilla: Extensive damage with one person confirmed dead
- Puerto Rico: More than 6,000 residents of the US territory are in shelters and many more without power. At least three people have died
- British Virgin Islands: Widespread damage reported, and five dead
- US Virgin Islands: Damage to infrastructure was said to be widespread, with four deaths confirmed
- Haiti and the Dominican Republic: Both battered by the storm, but neither had as much damage as initially feared
Another hurricane, Jose, has been weakening over the western Atlantic, with swells due to affect parts of Hispaniola (the island split into Haiti and the Dominican Republic), the Bahamas, and the Turks and Caicos Islands, over the next couple of days.