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."