The image was shared with the hashtag #sedonadreams and later removed from Instagram.
Hudgens paid the $1,000 fine after being cited for a misdemeanour count of damaging a natural feature on US Forest Service Land, according to the Associated Press. She also directed officials to the location of the carving.
A copy of the agreement, which was not made public, was obtained by AP.
The amount paid in the fine was used to restore the rock wall.
The media attention brought to the image alerted the Coconino National Forest, which looks after land around Sedona.
Coconino National Forest Service spokesman Brady Smith said: “She was caught in the act because she publicised it and she’s famous. I’m sure there are others who are not famous and publicised it and we’ve never known.”
Representatives for Hudgens did not immediately respond to a request for comment.
