The father was taken to hospital with unspecified injuries.
The reports came just hours after Florence made landfall as a Category 1 hurricane at 7:15am local time (11:30 GMT) at Wrightsville Beach, a few miles east of Wilmington, as the centre of its eye moved onshore, the National Hurricane Center said. Through the day, the storm's pace slowed even more, from 10 miles per hour Thursday morning to 3 miles per hour by Friday evening.
Forecasters said Florence's surge could cover all but a sliver of the Carolina coast under as much as 3.4 metres of ocean water, and days of downpours could unload more than 0.9 metres of rain, touching off severe flooding.
Hundreds of people needed to be rescued after becoming trapped in their homes by a storm surge of up to three metres in New Bern, a town of 30,000 in North Carolina at the confluence of the Trent and Neuse rivers.
A tornado watch was also in effect for parts of North Carolina.
New Bern resident Dan Eudy said he and his brother were awakened on Thursday night by the sound of a boat ramming against his front porch.
Cooper said the hurricane was "wreaking havoc" on the coast and could wipe out entire communities as it makes its "violent grind across our state for days".
Food Lion, Bi-Lo, Aldi, Lidl, Kroger, Harris Teeter, Walmart and Publix were among the chains announcing temporary store closures in North Carolina, South Carolina and Virginia as Florence passes through the region.
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A fourth person reportedly was killed while plugging in a generator in the state's Lenoir County, according to U.S. media.
Forecasters are predicting that the storm will continue to weaken but still dump potentially record-breaking amounts of rain as it moves slowly inland.
At least 150 people were waiting to be rescued in New Bern, N.C., officials tweeted Thursday evening.
The National Hurricane Center said a gauge in Emerald Isle, North Carolina, reported 6.3 feet (1.92 meters) of inundation. Federal officials say they don't want people to fear going to shelters.
"I've never been one to leave for a storm but this one kind of had me spooked", he said.
"And it's just a Category 1 hurricane", Tarr said. It is expected to move across parts of southeastern North Carolina and eastern SC on Friday and Saturday, then head north over the western Carolinas and central Appalachian Mountains early next week, the NHC said.
Florence was seen as a major test for the Federal Emergency Management Agency, which was heavily criticized as slow and unprepared a year ago for Hurricane Maria in Puerto Rico, where the storm was blamed for almost 3,000 deaths in the desperate aftermath.
More than 700,000 people were left without power and millions more were warned by the governor of North Carolina that they were facing "an extremely unsafe situation".
A mother and infant in North Carolina were among the first reported fatalities linked to Hurricane Florence.