The jury reached the verdict after Sammantha Allen, 29, was convicted in June of first-degree murder and four counts of child abuse in the 2011 killing of Ame Deal, who was punished for stealing an ice pop.
Allen held her head in her hand and wept as the verdict was read and later cried and hugged her attorneys before she was led out of the courtroom.
"Lack of remorse was the biggest thing that played into it for us, that we didn't see that from Sammantha throughout the whole process," juror Anne Schaad told KTVK-TV.
Allen will become the 55th woman condemned to die nationwide. There are only two other women on death row in Arizona, which is among the states struggling to buy execution drugs after pharmaceutical companies began blocking the use of their products in lethal injections.
In comparison, nearly 2,800 men are facing executions in the U.S., according to an April report by the NAACP that's used by the Death Penalty Information Center.
In Allen's case, authorities said she and her husband are responsible for making Ame get into the box, where she was left and found dead six or seven hours later.
The girl's death was the culmination of a history of abuse that a handful of relatives heaped on her, authorities say.
Ame was forced to eat dog feces, crush aluminum cans barefoot, consume hot sauce and get in the storage box on other occasions. She also was kicked in the face, beaten with a wooden paddle and forcibly dunked after being thrown in a cold swimming pool, investigators said.
Adults at the home originally claimed Ame hid during a late-night game of hide-and-seek and wasn't found until hours later. Three other relatives are in prison serving sentences for abusing Ame.
Allen's husband, John Allen, 29, is scheduled to go on trial Oct. 9. He has pleaded not guilty to first-degree murder and child abuse and also faces the death penalty.
Sammantha Allen's mother, Cynthia Stoltzmann, who also was Ame's legal guardian, is serving a 24-year prison sentence for a child abuse conviction.
Child welfare authorities in Arizona said they didn't receive any reports of abuse before her death. But child welfare reports from Utah, where the family lived before moving to Phoenix, listed Ame as an abused child, police said.
The verdict comes after executions in Arizona were put on hold following the 2014 death of a prisoner who was given 15 doses of a two-drug combination before he died in what his attorney called a botched execution.
But the state is now able to resume executions after a lawsuit that challenged the way Arizona carries out the death penalty was settled earlier this summer. No executions are scheduled.