A Texas judge said on Tuesday that she would order the Infowars fabulist Alex Jones to pay the entire $49 million verdict a jury had awarded to the parents of a Sandy Hook school shooting victim, despite a Texas law capping punitive damages at far less than the amount jurors had allotted.

In August, a jury in Austin, Texas, ordered Mr. Jones to pay Scarlett Lewis and Neil Heslin, whose son Jesse Lewis died in the massacre in Newtown, Conn., $4 million in compensatory damages and $45 million in punitive damages after Mr. Jones spread lies that the shooting had been staged and that the parents were actors. Texas law caps punitive damages at two times economic damages plus $750,000 per plaintiff, which a lawyer for Mr. Jones, F. Andino Reynal, had predicted would limit the award to far less than the jury’s verdict.

But in a hearing on Tuesday, Judge Maya Guerra Gamble of the District Court in Travis County, where Infowars is based, questioned the constitutionality of the Texas cap, and called the verdict “a rare case” in which the emotional damage inflicted on Ms. Lewis and Mr. Heslin was so severe that “I believe they have no recourse.”

Mr. Jones is likely to appeal, but the award is only a small part of a deluge of damages he is facing for the conspiracy theories he spread through his Infowars media empire about the 2012 shooting at Sandy Hook Elementary School. With a Connecticut court awarding more than $1.4 billion to the families of eight Sandy Hook victims this fall, Mr. Jones already faces financial ruin, and it remains unclear how much money the families will ultimately collect.