Chief Dyer said the girl made a threat on Snapchat to shoot up the school and posted a picture that showed a Walmart display case - with several rifles inside it.
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On the photo was a message that read, 'Don't come to school tomorrow'.
The FBI alerted the Fresno Police Department to the threat and an officer followed the student, who was on the bus to school. She was pulled out of class and admitted to making the threatening post, according to Fresno Police.
Dyer said she said she snapped the photo because in order for her to continue to use this site there had to be so many posts made.
The student has been arrested and charged with making a terror threat.
Video: Fresno Police press conference on the arrest
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Authorities said after an investigation, it was determined that the threat was not credible.
A pellet gun was found in the student's home.
Fresno police say the aunt of the teenager was aware of the post and was disturbed by it. However, she did not alert authorities.
Superintendent Bob Nelson said there was nothing in the student's profile that would indicate concern.
He described her as a "very successful student enrolled in a robust course taking pattern."
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But Nelson wanted all Fresno Unified students to know this type of behavior will not be tolerated.
"Whether it's terrorist threats, sexting, vulgarity, bullying - all of that on social media is immediately trackable back to you, don't be naive about it."
It was a frightening start to the first week of school that involved every parent's worst fear.
"As a parent, you are always concerned about your child."
That concern for Rogenia Cox multiplied on Thursday afternoon after she picked up her daughter at Edison High School and learned of the threatening message.