Earlier on Friday, Jones was ordered to pay $4.1 million in restitution to the parents of one of the children killed in the massacre.
In December 2012, a 20-year-old man forced his way into Sandy Hook Elementary School in Newtown, Connecticut, and shot and killed 20 young children and six adults. The perpetrator then also murdered his mother before committing suicide.
For years, Jones spread false claims through his website Infowars and popular podcasts that Sandy Hook never happened.
Courts in Texas and Connecticut have already found Alex Jones guilty of libel for describing the massacre as a hoax staged by actors with the aim of curtailing gun rights in the United States. Followers of the conspiracy theorist have harassed and threatened to kill relatives of the victims.