Terrifying videos from the state have shown a gas station tipping over and acar being flipped into the air by a huge gust of wind.
The storm has now made its way inland through Georgia and the Carolinas.
At least three people have died after the hurricane made landfall in the US, officials have confirmed.
Two men were killed in separate weather-related road incidents in Florida, the state's highway patrol said.
A man in Georgia was killed by a falling tree while he was trying to clear another tree off a highway.
Mr DeSantis has warned looters who may try to target affected communities in Florida that they may be shot as recovery efforts got underway.
Idalia is expected to chart its path out into the Atlantic on Thursday, the National Hurricane Center said.