The attack came Thursday afternoon in the Cherokee National Forest in southeastern Tennessee.
The family was at a pool below Benton Falls on Chilhowee Mountain when the bear attacked, the Tennessee Wildlife Resources Agency said.
Witnesses told authorities the bear picked up the boy in its mouth while the mother and other visitors tried to fend it off with sticks and rocks, said Dan Hicks, a spokesman for the Tennessee Wildlife Resources Agency. The mother and the boy were critically injured and flown to Erlanger Medical Center in Chattanooga, authorities said.
When the bear attacked, the 6-year-old girl ran away, authorities said. Rescuers found the girl's body about 100 yards down the trail from the falls. A bear was standing over her.
"Allegedly, after the rescue squad found the little girl, one of the squad members fired a shot from a small caliber handgun," Hicks said Friday. "We don't know whether the bear was hit or not. There was no blood, but it chased it off."
Hicks said authorities were using dogs and set traps baited with honey buns and doughnuts. Wildlife officers planned to put out more traps Friday morning, he said.
The 640,000-acre park runs along the Tennessee-North Carolina line southwest of Great Smoky Mountains National Park.
Rangers said black bears rarely attack humans and that the animal may have been suffering from a disease that affected its behavior.
"It's a pretty rare thing, black bears generally don't attack people. I can't think of any time other than, just really rare circumstances," said Monty Williams, park ranger.
In May 2000, a woman was killed by a black bear near Gatlinburg. Glena Ann Bradley, a schoolteacher from Cosby, was attacked by two female bears when she took a walk on a trail near a Smoky Mountains campground.