Two officers who had been helping at an evacuation shelter were killed in a vehicle crash in Hardee County, officials say.
The hurricane center says "although weakening is forecast, Irma is expected to remain a hurricane at least through Monday morning".
A few hours later, it was downgraded again to Category 2, with maximum sustained wind gusts of 175 kph, the National Hurricane Centerreported in Miami.
The storm was earlier pummelling the area around the city of Fort Myers.
Irma, one of the most powerful hurricanes ever seen in the Atlantic, has already killed 28 people in the Caribbean.
The massive storm triggered evacuation orders for 5.6 million people, and made two landfalls Sunday.
The below video, from Twitter user Bryan Woolston, shows heavy rains and winds tearing through Florida's trademark palm trees.
At 03:00 GMT, the centre of the hurricane was about 80km south-east of the city of Tampa. The region has not been hit by a major hurricane since 1921.
President Donald Trump approved a "major disaster" declaration in Florida on Sunday, authorising "federal funding to flow directly to Floridians impacted by Hurricane Irma".
Storm surges, especially after the early morning high tide, were expected to bring up to 15 feet of water flooding inland in the Tampa area.
How did it arrive in Florida? The first landfall in the United States occurred at 9:10 AM at Cudjoe Key, Florida.
"I'm heading down to the Keys now with the Coast Guard to assess the damage there with the storm surge", Scott said. Naples was struck with 228km/h winds, almost 12 inches of rain and had a 7-foot storm surge. As for effects in the mainland USA, forecasts so far expected only tumultuous surf and rip current conditions on the east coast. Utilities have invested billions into strengthening the power grid in recent years, but the improvements aren't enough to resist Irma's strong winds, the Wall Street Journal reports.
Overall, more than 13,000 flights have been canceled in Florida and the Caribbean thus far as a result of the storm, according to Flight Aware.
The hurricane watch from north of Fernandina Beach to Edisto Beach has been discontinued.