The decision came after a hearing Friday at which one of Gilberto Valle's alleged targets opposed a motion to grant bail, the New York Post reported.
Michelle Mechanic, a lawyer for Victim No. 2 -- as her client is called -- told the judge she fears Valle would come after her if he is released, the newspaper said.
"My client is not sleeping," Mechanic said. "She's frightened and has confined herself to her home with her mother."
Valle allegedly planned a campaign to kill as many as 100 women. Federal investigators said he was involved in an email exchange with a man who wanted to rape and kill a woman after Valle abducted her.
Notable deaths of 2014 [PHOTOS]