Residents have already begun stocking up on supplies, with superstore shelves running empty of essentials such as bread, milk, and batteries, and cars forming long lines at gas stations.
"It's a good that [people] are actually paying attention to the storm and are being prepared," said 45-year-old Stacie Klein, from Delray Beach, Florida.
According to Klein, three stores in her area had been depleted of essential supplies Tuesday.
"If things look too bad, it's hotel bound for me," she added. "I'm glued to the TV and have notifications and alerts sent to my phone."
Similar shortages were reported in other parts of Florida and in Charleston, South Carolina.
Matthew has been churning its way through the Caribbean this week, causing widespread damage across Haiti before making landfall in in Cuba around 8 p.m. ET Tuesday.
The hurricane was packing 125-mph winds as it took aim at the Bahamas early Wednesday.
The storm is likely to bring high winds and heavy rain to Florida on Thursday, before crawling its way up the coast toward Georgia and the Carolinas by Friday or Saturday.
"Only a small deviation of the track to the left of the ... forecast could bring the core of a major hurricane onshore, while a small deviation to the right could keep all of the hurricane-force winds offshore," the National Hurricane Center said Tuesday.
The Weather Channel said it was "becoming an increasing possibility" that Matthew would get close enough to bring hurricane-force winds to the East Coast states.
"Regardless if there is a direct hit or not, the impacts will be devastating," Florida Gov. Rick Scott said. "I cannot emphasize it enough that everyone in our state must prepare now for a direct hit."
Scott has activated 200 members of the National Guard to support hurricane response and said 300 more would be staged across the state Wednesday.
South Carolina Gov Nikki Haley said that unless the storm's course changes dramatically, officials will start to evacuate 1.1 million of the state's 4.8 million people at 3 p.m. ET Wednesday.
"We don't do voluntary or mandatory. It is an evacuation," Haley said at a news conference. "Our goal is to make sure you get 100 miles away from the coast."