Officials didn't provide her name.
Bergin didn't know if she's a tourist or a Hawaii resident. "The shark is still in the area, so we're trying to get people out of the water at this time," he said.
Police said witnesses described the shark as having a gray tip. Bergin said he was told it's possibly a 6-foot (1.8-meter) black-tip reef shark.
The bay will remain closed until at least noon Wednesday. Shark warning signs were posted on both sides of Kealakekua Bay State Historical Park.
"According to local fishermen, this time of year there's a lot of fish in the area, so it does attract a lot of sharks and dolphins birthing," Bergin said.
The high surf also makes for poor visibility in the water, he said.
This was the ninth shark encounter reported by state officials this year, including one that was fatal. A 65-year-old man from California died after a shark bit him while he was swimming off a Maui beach park in May. Last week, a surfer in turbid water off Oahu's west coast escaped injuries when a shark chomped on his surfboard.
There were three incidents reported last year and five in 2017.