The agency said that "plant procedures require operators to shut down the reactor well before hurricane-force winds arrive on site".
President Trump declared states of emergency for North and SC and Virginia, opening the way for federal aid.
Operators of nuclear plants in the Carolinas and Virginia are preparing for Hurricane Florence, which is expected to make landfall in the south-east of the United States of America later today.
Speaking during a visit to Moscow less than an hour after the hurricane made landfall in North Carolina, Perry said "we've done this many times before".
The Union of Concerned Scientists, said it was anxious about the Brunswick plant's capabilities to weather out the storm.
Brunswick is located about four miles (6.4 kilometers) from the coast and sits about 20 feet (6.1 meters) above sea level.
Watch South Carolina BATTERED by gale force winds
By Friday evening, Florence was downgraded to a tropical storm, its winds weakening to 70 miles per hour as it pushed inland. Officials said some 1.7 million people in the Carolinas and Virginia were warned to evacuate, but it's unclear how many did.
One of the many areas of concern for regions facing a storm of the scope of Hurricane Florence are nuclear power plants - especially in the aftermath of the 2011 Fukushima Dai-ichi disaster in Japan.
He added: "Those power plants are, one, obviously hardened".
Flooding at nuclear plants became more of a concern after a 2011 quake and subsequent tsunami in Japan caused one of the worst nuclear disasters since the 1986 Chernobyl incident.
According to the group, the Nuclear Regulatory Commission has not released public information validating that the plant has been properly updated to protect against flooding.
Duke Energy Corp spokeswoman Mary Kathryn Green told Reuters that since the accident at the Fukushima nuclear plant in Japan in 2011, all USA nuclear plants have installed more safety equipment, including portable pumps and generators.
In preparing for Hurricane Florence, the NRC statement said that the staffs at Brunswick, Surry in southeastern Virginia, Harris near Raleigh, N.C., Robinson near Hartsville, S.C., and some other plants are working through their severe weather procedures, including ensuring that all loose debris and equipment have been removed or secured, and conducting walk-down inspections of important systems and equipment. The storm will be the first major hurricane of the season and will show how the sector responds after a trio of storms tested utility systems in Florida, Texas and Puerto Rico previous year - leaving some on the island without power for months.