Benito and Carol Gutierrez are accused of keeping the four children, aged between six and 12, locked in rooms with no light or food.
Police were alerted when one boy left the house in Tucson.
He entered a shop to call a relative, but an employee called police because of concerns about the boy's appearance.
The Pima County Sheriff's Department said they discovered that the children "were kept in separate bedrooms, which were locked from the outside, with no access to food, water, lights, or bathroom facilities for up to twelve hours at a time on a regular basis".
