The attack took place near a pool of water on Chilhowee Mountain, said Dan Hicks, spokesman for the Tennessee Wildlife Resources Agency.
Witnesses described the bear picking up the boy in its mouth while the mother and other visitors tried to fend it off with sticks and rocks, Hicks said. The mother was injured before the bear was chased away.
The girl ran away during that attack, but was found dead a short time later with the bear nearby. A park ranger fired at least one shot at the bear before it bolted off.
The woman and her son were flown by helicopter to Erlanger Medical Center in Chattanooga, where both were being treated for wounds consistent with a bear attack, Hicks said.
Hospital officials did not immediately return calls for comment, but Hicks said the boy was listed in critical condition. The victims' names were not released.
Forest Service employees, TWRA game agents and several hunters were searching for the bear in an area spanning several thousand acres.
The 640,000-acre park runs along the southeastern Tennessee border with North Carolina, southwest of Great Smoky Mountains National Park
