Prosecutors said that as a result of that post, made right before Clinton was set to begin a book tour, the Secret Service both launched an investigation and "expanded significant additional resources to ensure Secretary Clinton's protection."
Shkreli amended his Facebook post about Clinton's hair after it garnered widespread attention, writing that it was "satire, meant for humor."
But prosecutors noted that Shkreli has longstanding animus toward Clinton, pointing out that he traveled on Sept. 11, 2016, to stand outside of Chelsea Clinton's apartment after learning Hillary Clinton had been taken there after fainting following a 9/11 memorial ceremony.
"Shkreli ... stood outside an apartment owned by Secretary Clinton's daughter where she was recuperating, and spent approximately two hours live-streaming while providing commentary and heckling Secretary Clinton," the prosecutors wrote.
Prosecutors also wrote that through his lawyer, "Shkreli also conveyed to the government and to the Secret Service that he would remove the original [Facebook] post regarding the threat to Secretary Clinton on September 5, 2017; however, he declined to do so until late in the day on September 6, 2017."
In addition to the post about Clinton, the motion also cites public statements "harassing specific women" during his trial.
One of those women was journalist Lauren Duca, whose prior harassment by Shkreli got him banned by Twitter earlier this year, and the other was political pundit Anna Kasperian.
On Facebook in late July, "on the eve of the final trial summations," Shkreli wrote, " 'Trial's over tomorrow b-----. Then if I'm acquitted, I get to f--- Lauren Duca ... And Anna Kasperian' '" prosecutors noted in their motion.
"Thus, just as the case was to be submitted to the jury, Shkreli made a public threat against two women whom he dislikes and with whom he has feuded in the past," prosecutors wrote.
"Shkreli's own prior actions, and his influence over others who have previously acted in reliance on his statements, demonstrate why the government views his latest actions with concern."
The prosecutors' motion says, "The government respectfully submits this motion for a bail revocation hearing, at which the government will move to revoke the defendant Martin Shkreli's bail and remand him into custody."
"His recent public conduct demonstrates that he cannot meet his post-trial burden to show, by clear and convincing evidence, that he does not pose a danger to the community," the prosecutors from the Eastern District of New York wrote.
Since his conviction on August 4, 2017, Shkreli has engaged in an escalating pattern of threats and harassment that warrant his detention pending sentencing. Most recently, Shkreli threatened former Secretary of State Hillary Clinton by publicly offering$5,000 to anyone who would "grab" some of her hair on the defendant's behalf during her upcoming book tour. In a post-trial posture, it is Shkreli's burden to show that he should befree on bail pending sentencing. Shkreli's latest threat is concerning not only because it has required a significant expenditure of resources by the United States Secret Service, which is charged with protecting Secretary Clinton, but also because there is a significant risk that one of his many social media followers or others who learn of his offers through the media will take his statements seriously—as has happened previously—and act on them. His late actions constitute changed circumstances that show that he cannot meet his burden of showing that he should remain at large pending sentencing.
"The defendant's threats create a risk of danger to the community," prosecutors wrote. "And they are certainly not appropriate behavior for a defendant who has been found guilty of securities fraud and conspiracy to commit securities fraud—a defendant whose detention is presumed under the law.
John Marzulli, a spokesman for the prosecutor's office, declined to comment on the filing.
In addition to trolling Clinton on Facebook, Shkreli this week began an auction of the single copy of the Wu-Tang Clan album "Once Upon a Time in Shaolin" on eBay. Shkreli himself had bought that album by the hip-hop group for a whopping $2 million in a 2015 auction.
As of Thursday, bidding on the album had topped $1 million.
Shkreli first gained public notoriety in mid-2015 when the company he then headed, Turing Pharmaceuticals, raised the price of an anti-parasitic drug called Daraprim by more than 5,000 percent.
He was arrested in late 2015 on charges unrelated to the Daraprim price increase. Prosecutors claimed Shkreli had defrauded multiple investors in two hedge funds he previously ran, and then looted another drug company he founded, Retrophin, to pay back those investors.
Although he was convicted of securities fraud charges that could land him in prison for several years or more, Shkreli was acquitted of other charges that could have resulted in significantly more time behind bars.
WATCH: Co-worker says Shkreli 'mentally unstable'