"The individual we believe to be responsible for the social media post has been detained and the investigation is ongoing", law enforcement officials told TMZ.
The LAPD is investigating the threat, but it is unclear if authorities have made contact with the former student.
"Hashtags of "#MiamiDolphins" and "#HarvardWestlake" were included on the image of the shotgun.
Albarran said they were notified of the Instagram post Thursday night, which was made by a student who attended the school about a decade or so ago.
Harvard Westlake shut classes down on Friday amid the threat.
Harvard-Westlake high school also released a statement to explain why the school was closed on Friday. "We are working closely with law enforcement and will share more information when we are able".
The report also mentioned that Martin contemplated suicide on at least two occasions.
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I've seen the development of the auto for the last eight months and so to see all the pieces come together, it's a work of art. I wouldn't write anybody off. "It's very unsafe before the season has started to reduce the number of potential competitors".
Martin's disturbing post comes just a week after a lone gunman opened fire in a Florida high school, killing 17 students.
More than 100 students marched from Blake High School to downtown's Curtis Hixon Park on Friday in a Parkland school shooting-inspired protest aimed at lawmakers in Tallahassee.Dozens more joined them along the way, and the crowd swelle.
After leaving the Dolphins, Martin spent one season with the San Francisco 49ers, appearing in 15 games and starting nine.
Martin, who played offensive tackle for the Dolphins, reportedly checked into a hospital for emotional distress over the incident, and returned to his parents home in California. He later admitted he suffers from major depressive disorder and anxiety.
Martin, who underwent counseling for emotional issues after the bullying scandal, posted on Facebook in 2015 that difficulties in football led him to attempt suicide multiple times. He did not play in 2014 and resumed his career in 2015 with the Buffalo Bills, where he has played the past three seasons.
Martin's Instagram is private, but a screencap of the alleged post has been circulating on social media.