Police confirmed the fatalities on Twitter, saying the father of the child was being transported to a local medical centre to be treated for his injuries.
U.S. media later said a second man in Lenoir County died after heavy winds knocked him down as he tried to check on his dogs.
A day after Florence's landfall in North Carolina, water is shaping up to be the storm's deadliest impact - and the rains will only keep coming as flood damage mounts. Over 60 people had to be pulled out of a collapsing motel in Jacksonville, North Carolina, and hundreds were saved as water levels rose.
Morehead City, North Carolina, had received 23 inches (58 centimeters) of rain by Friday night, and forecasters warned Saturday morning that parts of the Carolinas could get up to 15 inches (38 centimeters) more.
Florence has already knocked out power to close to a million households in the Carolinas, with some areas not expecting to regain electricity for days.
Authorities in New Bern, a town of about 30,000 people that dates to the early 18th century, said more than 100 people had to be saved from floods and that the downtown area was underwater.
"We're not going to be satisfied until the last resident is rescued and in a shelter, and then we can assess damages and go from there", New Bern Mayor Dana Outlaw said, according to the Herald Sun of North Carolina.
"Our hearts go out to the families of those who died in this storm", Cooper said in a statement on Friday. "These are folks who are maybe in one-story buildings and they are seeing the floodwaters rise".
The White House said President Trump will tour areas affected by Florence next week, once it is determined that his visit will not disrupt rescue and recovery operations.
People walk past a tree uprooted by strong winds lies across a street in Wilmington, N.C., after Hurricane Florence made landfall Friday, Sept. 14, 2018.
"[It's] very eerie, the wind howling, the rain blowing sideways, debris flying", Orsa, who lives nearby and fears splintering trees will pummel her house, told The Associated Press.
"It's insane", he said in a phone interview. "You can never predict what a hurricane is going to do but I'm just not going to run away from this".
Tropical storm Florence moved slowly down the Carolina coast on Saturday, as officials forecast catastrophic flooding in the region and said at least five people had been killed by the giant weather system that is set to plague the area for days ahead. The storm knocked out power to almost 930,000 homes and businesses, and the number could keep rising.
Gibson said she thinks some people couldn't afford to evacuate New Bern and others didn't heed evacuation warnings after Florence dropped from a Category 4 to a Category 1.
North Carolina Governor Roy Cooper had said that "several more days of rain" were expected, describing the amount of rainfall from the hurricane as a "1,000-year event".
"The cost to SC, if that happens, if the storm continues the way it is going, could be in the billions", Dahler said.
Onslow County, located about 50 miles to the northeast of Wilmington, has been hit particularly hard.