He said that storm surges in coastal areas could be as high as 12ft (3.7m), adding that people "cannot survive this".
Some 50,000 people have gone to shelters throughout the state, the governor said. Media reports say shelters in some areas have been filling up quickly and some people have been turned away.
Miami city and Broward county have imposed curfews to help clear the roads of traffic.
Which other areas have already been hit?
Cuba: Officials have reported "significant damage", without giving further details, but said there were no confirmed casualties yet, the AFP news agency reports
St Martin and St Barthelemy: Six out of 10 homes on St Martin, an island shared between France and the Netherlands, now uninhabitable, French officials say. They said nine people had died and seven were missing in the French territories, while two 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