The judge agreed with prosecutors that Shkreli, who claimed the offer was a satirical joke gone bad, was a threat to the public because of both that bounty and because of other online posts he wrote disclosing his intent to "f---" two women after his trial ended.
Since then, Shkreli, 34, has been in jail at the Metropolitan Detention Center in Brooklyn, awaiting sentencing in January for his conviction on securities fraud charges.
His lawyer Brafman on Monday filed a motion asking that Matsumoto release restrictions on an E-Trade brokerage account that was securing Shkreli's $5 million release bond. Matsumoto has yet to rule on that motion.
CNBC has reached out to Brafman for comment on the psychiatric exam motion.
John Marzulli, spokesman for the United States Attorney's Office for the Eastern District of New York, which prosecuted Shkreli, declined to comment Wednesday.
During Shkreli's trial it was revealed that a former employee of his hedge funds once had referred to him as "mentally unstable" in an online chat she had with an executive at the fund.
The ex-employee, Caroline Stewart, testified that she had believed Shkreli was mentally unstable because "in my opinion it's crazy to lie so much, particularly about things that are easily uncovered."
Stewart also testified that Shkreli was "deeply depressed" in February 2011 after his hedge fund effectively "imploded" and was left owing $10 million to Merrill Lynch from a failed short sale of stock.
Other testimony and evidence at Shkreli's trial showed him repeatedly lying to hedge fund investors about his performance managing their money, and then scrambling to pay them back for their lost money with cash and stock from a drug company he founded, Retrophin.
Shkreli was convicted in early August of three securities fraud counts and acquitted of five other charges.