The father was taken to hospital with unspecified injuries.
Nearly 800,000 people are reported to be without power already in North Carolina, and officials have warned restoring electricity could take days or even weeks.
Super Typhoon Mangkhut tore through the northern tip of the Philippines on Saturday packing winds of more than 200 km per hour (124 mph) along with torrential rain, killing three people and causing floods, landslides and power outages.
Forecasters have been predicting catastrophic flash flooding.
The National Hurricane Center said a gauge in Emerald Isle, North Carolina, reported 6.3 feet of inundation.
In Jacksonville, North Carolina, officials rescued about 60 people overnight from a hotel that was collapsing in the storm.
"WE ARE COMING TO GET YOU", the city tweeted around 2 a.m. "You may need to move up to the second story, or to your attic, but WE ARE COMING TO GET YOU", the New Bern authorities said on Twitter.
More than 500,000 customers were without power, mostly in North Carolina, as the eye of Hurricane Florence went ashore near Wilmington and began its slow trek along the coast, according to poweroutage.us.
As it moves inland, the storm is expected to bring its high winds and intense rain bands across the southeastern corner of North Carolina and a large chunk of SC. It was crawling west-southwest at 3 miles per hour, lifting huge amounts of ocean moisture and dumping it far from the coast.
The sixth Florence related death is also the first reported in South Carolina, according to both the South Carolina Highway Patrol and the Union County Coroner's Office.
Rivers are rising on the north side of Hurricane Florence as the storm swirls counter-clockwise, pushing a surge of ocean water far in from the coast.
"This is an uninvited brute that just won't leave", he told NBC.
Florence has dumped more than a foot of rainwater on parts of southeastern North Carolina since making landfall near Wrightsville Beach at 7:15 a.m. ET.
Forecasters say Florence is now a tropical storm but will continue to threaten North and SC with powerful winds and catastrophic freshwater flooding. It started pushing its way westward across SC later in the day, in a watery siege that could go on all weekend.
Preparing for the worst, about 9,700 National Guard troops and civilians were deployed with high-water vehicles, helicopters and boats that could be used to pluck people from the floodwaters.
Authorities warned too of the threat of mudslides and the risk of environmental havoc from floodwaters washing over industrial waste sites and pig farms.
Florence is going southwest after landfall.
Tom Balance, owner of a seafood restaurant in New Bern, had decided against evacuating his home and was soon alarmed to see waves coming off the Neuse and the water getting higher and higher. "There are a deficit of cots not only in New Hanover County but I would suggest throughout eastern North Carolina". Pleasant was one of the few people out walking Friday morning on Market Street, where downtown shops typically teeming with tourists were boarded up and fortified with sandbags.
He said 20,000 people were being housed in shelters across the state.
Tropical storm-force winds extend outward up to 175 miles from its center. More than five million people are in the path of Super Typhoon Mangkhut, officials say.
Another woman who was rescued by another group in New Bern told CNN's "Anderson Cooper 360˚" that she and her family thought they would be safe in their brick home and heard the storm had been downgraded from a Category 4.
"The infrastructure is going to break", Long said Thursday morning.
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