The girl, who Dallas police say gave a false name and birthday, was released on probation before her true age was discovered, the newspaper reported.
"That's no place for a juvenile to be," Lt. Andy Harvey said. "There are adults in there; that's why we have places set aside for juveniles."
The girl told police she was 17-year-old Michelle Washington and pleaded guilty to the theft charge before a magistrate judge.
But the arresting officer, Senior Cpl. Roberto Garcia, said the girl initially told him she was 14.
"It is challenging at times, because we speak to so many people out here, and a lot of them don't have IDs and those kinds of things, and so we have to find ways and be creative a lot of times (to) try to get people's true identities," Harvey said.
But Assistant Chief Ron Waldrop told the Dallas Morning News there are "unanswered questions" about why officers did not verify her identity after she gave different ages.
"Everybody believes that should have required an intense level of checking before incarceration," he said.
An inmate who is an acquaintance of the girl's family recognized her and contacted the 13-year-old's father. He provided police with a birth certificate and other records that verified her real identity and age.
Her father told the Dallas Morning News that a 13-year-old doesn't belong in jail alongside adults.
"They could have killed her," he said. "Something bad could have happened. She doesn't look 17. She looks 13, and I wonder why they didn't see that."
Dallas police have launched an internal affairs investigation to review the incident.
The girl, who had run away from home, was arrested July 10 at a Target in Old East Dallas. She and a 20-year-old woman were allegedly caught smuggling clothes, candy and lingerie out of the North Haskell Street store, according to a police report.
She was released from custody July 23 and is again listed as a runaway.
Sgt. Warren Mitchell told The Associated Press that investigators want to find out if Garcia followed policy and what can be done to prevent the situation from happening again.