According to ESPN, Martin was detained because of the post.
"When you're a bully victim & a coward, your options are suicide or revenge", Martin wrote over a photo posted Thursday on his verified Instagram account. He used the hashtags #HarvardWestlake and #Miami Dolphins.
It is not clear whether Mr Martin posted the picture himself.
A pair of Harvard-Westlake High School campuses, in Los Angeles suburbs Studio City and Beverly Crest, were closed Friday after a threat made on social media.
Kway said the department was unable to publicly confirm that Martin's Instagram stories post was what caused the shutdown. "He's not a threat anymore".
"The investigation is continuing, but rest assured we believe there is no threat to any school in the LA area", the LAPD said in a statement.
FILE - In this October 27, 2013 file photo, Miami Dolphins tackle Jonathan Martin sits on the bench in the first quarter of an NFL football game against the New England Patriots, in Foxborough, Mass. In August 2015, he said he attempted suicide on multiple occasions. The Dolphins selected Martin in the second round in 2012. The Patriots defeated the Dolphins 23-16.
The NFL published a 144-page report from attorney Ted Wells, which included a series of distressing text messages from Martin to his parents alleging bullying throughout middle and high school, at Stanford and in Miami.
Police are also in contact with the four people Martin tagged in the photo. While with the Miami Dolphins, he accused Incognito and other teammates of bullying.
Jonathan Martin while playing for the San Francisco 49ers. Martin left the Dolphins in 2013 after accusing teammates of bullying.
The report revealed Martin had been subjected to racist, sexually explicit, homophobic and misogynistic messages, and labeled his interactions with Incognito, who was suspended for eight games by the National Football League because of the investigation, as "harassment".
-Pouncy is still on the Miami Dolphins while Incognito plays for the Buffalo Bills.
"The individual believed to be responsible for the social media post is being detained, however he is not in police custody", the LAPD spokesperson Tony Im told USA TODAY Sports in an email on Friday night.
"All of his teachers loved him. I can see where somebody that's a bully will take advantage of him, and rather than him say anything would just hold it inside".