According to Unified Police Lieutenant Justin Hoyle, the girl and a 19-year-old boy were climbing the mountain when their rope got stuck.
A distress call came in after 5 p.m. on Sunday.
Hoyle said the boy was able to unhook himself and climb down to safety on his own, but the girl was stranded on a ledge.
After several hours, rescuers rappelled down to the girl and hooked her up to another rope. She was safely rescued without injuries.