River flooding caused the shutdown Friday of a natural-gas plant near Wilmington, N.C., after several breaches in a cooling lake were discovered and some waste tied to the facility’s past as a coal-fired plant entered waterways.

Duke Energy Corp. said Friday that the rising Cape Fear River overtopped the dam at a cooling pond next to a coal-ash landfill at its L.V. Sutton Power Plant. The plant burns natural gas after coal-fired units were retired in 2013.

The company believes the coal ash—which was about 5 feet below a steel wall at last check—is still contained, but Duke Energy spokeswoman Paige Sheehan said she couldn’t rule out the possibility that coal ash was moving into the Cape Fear River.

The Sutton Power Plant, near Wilmington, N.C. Photo: Alex Wroblewski/Bloomberg News

The company said another type of waste from burning coal to generate electricity—lightweight hollow beads of alumina and silica known as cenospheres—was entering the river, and environmental groups warned people to stay out of the affected water.

The company said the plant provides enough electricity to power 500,000 customers, but that customers would not be affected by the outage.

Friday’s breaches came in the aftermath of Hurricane Florence, which hit North Carolina a week ago bringing record rainfall over days. Rivers are continuing to rise.

Though Florence made landfall a week ago, the process of draining away the water the storm dumped on the region is proving painfully slow. Some rivers around the border of the Carolinas near the coast are still in major flood stages, or have yet to crest.

The Cape Fear River near the Duke Energy power plant was forecast to crest sometime over the next few days.

Duke Energy has been in the process of moving coal ash at the Sutton power plant from ponds into a lined landfill meant to store the material permanently. Environmental groups that sued the company to install the new system have expressed concern about the risks from storms and flooding.

Speaking at a midday press conference Friday, Michael Regan, secretary of the North Carolina Department of Environmental Quality, said water from Sutton Lake had spilled over into Duke’s transmission yard, prompting an evacuation there.

“What we don’t know at this point is if any coal ash has filtered into the Cape Fear River,” Mr. Regan said. He said the department was planning flyovers to check.

Ms. Sheehan said floodwaters have submerged one of two coal-ash basins that sit next to Sutton Lake—a 1,100 acre cooling pond built to support coal plant operations. The basin is separated from the cooling pond by a steel wall that has also been submerged.

The company said water was flowing out of the south end of Sutton Lake in a second breach, and that cenospheres are leaking into the Cape Fear River.

Cape Fear Riverkeeper Kemp Burdette said he was assessing the situation on-site Friday, and called any seepage of coal ash into the river a serious concern.

“Cenospheres are coal ash, so if cenospheres are moving into the Cape Fear River, then that means coal ash is moving into the Cape Fear River,” he said. If that happens, then floodwaters could be carrying metals like arsenic, boron and chromium, he said.

—Jon Kamp contributed to this article.

Write to Kris Maher at kris.maher@wsj.com and Erin Ailworth at Erin.Ailworth@wsj.com