Judge Barbara Bellis wrote in a court filing Friday that the FBI contacted Connecticut State Police about the threats, and that state police notified her. Bellis did not release details.
Twenty first-graders and six educators were killed in the 2012 shooting at Sandy Hook Elementary School in Newtown.
Eight victims' families and an FBI agent who responded to the shooting are suing Jones for defamation over comments made on his show about the shooting being a hoax.
A lawyer for Jones says that the threats don't appear to be serious, but that a review of the website was being conducted.