Farther up the coast, in New Bern, about 150 people waited to be rescued from flooding on the Neuse River, WXII-TV reported.
When all is said and done, Florence could dump 18 trillion gallons along its path, according to meteorologist Ryan Maue.
Nearly 20,000 people had taken refuge in 157 emergency shelters, Mr Cooper said.
Ahead of the storm's arrival, shelters animals were moved out of the states in the affected area to protect them.
Police in Wilmington, North Carolina, near where the hurricane made landfall, said a mother and her infant were killed when a tree fell on their house. Local media said she had suffered a heart attack.
"Our house is on high ground so we're not anxious about the flooding", he said.
"This storm is going to continue its violent grind across our state for days", Cooper said.
Over 645,000 power outages were reported Friday morning.
The White House said on Friday President Donald Trump would travel to the region next week unless his visit would disrupt cleanup and rescue efforts.
The National Weather Service has issued strong warnings to residents of the Carolinas and other mid-Atlantic states, saying the hurricane would be the "storm of a lifetime", bringing damaging winds, life-threatening storm surges, and "catastrophic flooding".
"Flash flooding will be extreme and flood waters will come up quickly and seemingly out of nowhere", the governor said.
Forecasters said Florence's surge could cover all but a sliver of the Carolina coast under as much as 11 feet (3.4 meters) of sea water.
Hurricane Florence made landfall in North Carolina Friday morning, bringing howling winds up to 90 miles per hour, reports The Associated Press. 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.
"This is not the end of it", said Jeff Byard, associate administrator for response and recovery at the Federal Emergency Management Agency (FEMA).
The flooding soon spread into SC, swamping places like North Myrtle Beach, in a resort area known for its white sands and multitude of golf courses.
Hurricane Florence has barrelled into the Carolina coast and moved inland, knocking down trees, overflowing rivers, dumping sheets of rain and leading to the death of five people before it was downgraded to a tropical storm still capable of wreaking havoc.
"Some say North Carolina is getting a break, but we are on the wrong side of this story", he said.