"It could be the worst part of this is still to come," Scott said after a morning briefing at the state Emergency Operations Center. "I'm really concerned about Jacksonville."
Large parts of Jacksonville and surrounding areas are low-lying and subject to storm surges and flooding, Scott warned.
The hurricane – with maximum sustained winds of 120 mph – lashed the coast as the sun rose Friday, with its eye located about 45 miles off shore of Cape Canaveral and Daytona Beach.
The system, forecast to head back towards Southeast Florida after approaching South Carolina this weekend, was moving to the northwest at 13 mph Friday morning, according to the National Hurricane Center.
Matthew knocked out power to more than 600,000 homes, and more than 22,000 people sought shelter after massive evacuations Thursday targeted more than 1 million residents.
One death in Florida is being attributed to the storm.
In Port St. Lucie, a 58-year-old woman reportedly suffered a heart attack after the county suspended emergency-service operations, according to TCPalm. Scott and state Emergency Management Director Bryan Koon said at the 9 a.m. briefing that they were unaware of any storm-related deaths.
Early Friday morning, at least 600,000 homes were without power. But preliminary reports from South Florida counties were encouraging, with little damage reported.
But Scott, who is expected to travel to impacted areas later today, warned Floridians not to be complacent.
"We're only halfway through. We're going to have more outages," Scott cautioned.
About 90 Florida Fish & Wildlife Conservation officers have already started performing search and rescue operations, and another 70 are on standby, the governor said.
"As the storm passes we're sending them in to do assessments of both property and people," Scott said. "They have not reported any issues yet."
The Florida Highway Patrol did not report any major road issues, and tolls that had been lifted remained suspended Friday, Scott said.
Some gas stations had experienced temporary shortages, but the state has "plenty of fuel," according to Scott.
The governor also said that there is still time for the storm, which pelted the coast of Florida's peninsula overnight, to potentially shift west on Friday and make landfall.
Winds from the storm on its initial northern run are expected to be felt in the state through early Saturday morning.
The system has been credited with 280 deaths in the Caribbean, and that number could grow.
With recovery efforts underway south of Brevard County after Florida's Southeastern coast was pummeled by Hurricane Matthew, Gov. Rick Scott warned Friday morning that the state is only halfway through the powerful storm.