The agency said that "plant procedures require operators to shut down the reactor well before hurricane-force winds arrive on site".
There are 16 reactors in North Carolina, South Carolina and Virginia, the states that likely will sustain the most damage from the storm, but most are located well inland and not expected to experience hurricane force winds.
The Brunswick plant is near Cape Fear and just south of Wilmington, North Carolina.
Hurricane Florence has been downgraded to a Category 2 storm, but the National Weather Service (NWS) warns it will still cause "life-threatening" storm surges and "catastrophic" flooding across parts of the Carolinas.
Nuclear plants have procedures that require they shut a safe amount of time before hurricane force winds of at least 74 miles per hour are expected to reach the site.
The Union of Concerned Scientists, said it was anxious about the Brunswick plant's capabilities to weather out the storm.
As Hurricane Florence churns its way towards the Carolinas, at least 8 nuclear power plants stand in its way.More news: Trump signs order for sanctions against foreigners who meddle in polls
The six nuclear power plants in North and SC sit directly in the storm's projected path, according to Mary Catherine Green, spokeswoman for Duke Energy, which owns all six.
Duke officials watching the storm's track on Thursday chose to close down the Brunswick plant, which is located about four miles from the coast.
About 485,143 people were without power in North Carolina as Florence made its way inward, according to the North Carolina Department of Safety.
He added: "Those power plants are, one, obviously hardened".
Diaz said he did not think there would be issues with the power plants in the upcoming storms.
With a major storm bearing down on these power plants, some thoughts are turning back to 2011, when Japan's Fukushima Daichi nuclear power plant was impacted in the wake of the devastating March 11 quake and tsunami.
NRC spokesman Scott Burnell said the Brunswick plant is properly fortified to withstand hurricanes of Florence's strength, and there are plans in place to shut down if necessary.
He said each plant has resident inspectors on site, and one or two additional inspectors at sites that are expected to be more directly impacted by the storm.