Martin, who was bullied by fellow offensive lineman Richie Incognito when the two were teammates in 2013, posted a photo of a shotgun and he tagged Incognito as well as another former teammate, Mike Pouncey.
The words "When you're a bully victim & a coward, your options are suicide, or revenge" appear in red letters next to the gun and shells.
Martin's account is verified, but private. The school closed amid the threats, with administrators telling students to stay off-campus as a precaution.
This is a developing story. In the year that followed, Martin indicated on social media that he attempted suicide during his National Football League career and that he never fit in at his high school.
It is unknown whether the Instagram account is Martin's account or if he posted the image.
One source at Harvard-Westlake said Martin has been detained over the incident, though police said there was "no credible threat" against students.
Martin's former agent told Business Insider that he no longer represents the former player, but called the situation a "sad story".
Martin's post also tagged two former students at Harvard-Westlake, as well as his former National Football League teammates Richie Incognito and Mike Pouncey. As a result, Incognito was suspended for the rest of the season and during the offseason, Martin was traded.
The school's campuses in Los Angeles are expected to remain open. We are working closely with law enforcement and will share more information when we are able.
In a message sent to students Friday morning, school officials said they were made aware of a "disturbing social media post that mentioned Harvard-Westlake by name" late Thursday night. Everybody is calm, a lot of people are leaving now, everything is under control.