The compensation is to be paid to the parents of one of the six-year-olds who was shot dead by a 20-year-old man who entered the school in December 2012.
The jury already determined on Thursday that Jones must pay $4.1 million in compensatory damages for the damage he caused through his claims.
On Friday, the jury awarded $45.2 million in punitive damages, which is a purely punitive measure.
The parents had sued Jones for 150 million dollars (1,534 million kroner).
Changed in court
Six adults and 20 children were killed in the massacre.
Jones, however, long spread the claim that the incident was made up and that survivors and relatives were actors - all with the aim of forcing tougher gun laws in the US.
Earlier this week, he finally admitted that the massacre took place.
The parents, in turn, testified about how they were persecuted and harassed by supporters of Jones.
"I can't describe the hell that I and others have gone through for the past nine and a half years because of Alex Jones' carelessness and ignorance," said father Neil Heslin, according to CBS News.
More processes are in progress
Alex Jones said during court proceedings that damages of more than $2 million will "sink" Infowars.
The parent company Free Speech Systems filed for bankruptcy protection a week ago.
However, an economist who reviewed the company's finances estimates that Alex Jones and Infowars together have assets of up to 270 million dollars.
Last year alone, Jones allegedly withdrew $62 million from the company.
Jones can count on additional claims for damages later this year.
Relatives who sued him for defamation have already been vindicated by a court in Connecticut and one in Texas.
However, the compensation amounts remain to be determined.