The raft buckled as it went over Bull Falls, north of Harpers Ferry, said Blue Ridge Mountain Fire Chief Scott Knill.
The girl fell out of the boat and injured her neck, Knill said.
Other boaters managed to get her to shore along a steep, wooded embankment below Jones Farm Lane, a private gravel road on top of Chestnut Hill.
The Shenandoah River is so low because of this summer's dry weather that it appears to hold more exposed rocks than water.
Firefighters from Blue Ridge Mountain and Friendship Fire Co. in Harpers Ferry hiked about a mile down a steep trail to the girl's location.
The girl's name was not released because of her age, fire and hospital officials said.
The girl was strapped into a stretcher with her head immobilized to protect her neck, fire officials said.
A team of firefighters started carrying the girl up the near cliff-like trail, Knill said.
Friendship Fire Co. Assistant Ambulance Chief Sean McCarthy said he looked at his watch, which also measures the temperature, and saw it was 96.4 degrees in a shaded area.
There also was no breeze in the woods and carrying the girl, even though she had a light build, took its toll on the firefighters, he said.
About halfway back up the trail, Blue Ridge Mountain Firefighter William Skinner suffered heat exhaustion, officials said.
The girl was taken on up to an ambulance and taken to the hospital while other medics worked on the downed rescuer, McCarthy said.
The medics started intravenous treatment to replenish the fallen man's fluids, McCarthy said.
Other firefighters cut brush to widen the foot trail enough to get the Blue Ridge Mountain Fire Co.'s brush truck down the path, Knill said.
The firefighter was taken up the path in the four-wheel drive truck and then transferred to another ambulance, Knill said.