The girl, Emily, had been receiving chemotherapy at Phoenix Children's Hospital for about a month, Phoenix police Sgt. Steve Martos said Monday.
An infection forced doctors to amputate her right arm and insert a catheter in her heart. The device was set to be taken out before her mother removed an IV from the girl, changed her clothes, and walked her out of the hospital Wednesday night.
Police said if the catheter is left in too long, it could lead to a deadly infection.
"If she contracts an infection, it really could just be a matter of days that could result in the young girl's death," Martos said. "It's pretty serious."
Authorities had been stymied by health privacy laws that kept them from releasing the parents' names, but police said Monday that U.S. Border Patrol stopped the girl's father, Luis Bracamontes, 46, as he crossed into Arizona from Mexico over the weekend.
Martos said the man provided no clues to the girl's whereabouts and denied having any involvement in removing her from the hospital. Police released his name, along with that of the girl's mother, Norma Bracamontes, 35, in hopes it will help locate the child.
Neither parent is charged with a crime yet, but authorities want the child brought back to the hospital before it's too late, Martos said.
He said the family lives a "nomadic" life without a permanent residence, but they have relatives in Arizona, California and Mexico, none of whom have been able to provide police with information about their whereabouts.
The girl's father is a Mexican citizen with a U.S. resident alien identification card. The child and her mother are U.S. citizens, Martos said.
Phoenix Children's Hospital spokeswoman Jane Walton declined comment, citing health privacy laws.
Authorities don't know why the child's parents took her from the hospital, but speculate they might have been concerned with paying the bill.
Surveillance footage shows the mother pushing an IV stand through a hospital hallway. The girl with her right arm removed above the elbow and wrapped in a bandage is seen walking beside her.
"We just don't know what their intent was," Martos said. "But this could become extremely serious if she contracts an infection ... Our primary concern is she get the proper medical care so we can prevent obviously the worst case scenario here."