Police say the girl and her younger sister had been placed in the care of the woman.
The girl broke free from a pole in the basement and walked to a police station for help.
Rocio Ochoa, 44, was arrested and charged with aggravated battery and unlawful restraint. Bond was set at $300,000.
Ochoa was appointed the girls' legal guardian in Arizona after the sisters' mother was deported to Mexico following a criminal conviction. Ochoa moved the girls to La Grange over a year ago.
Police say that on Monday just before midnight the girl walked six blocks from the duplex to the police station after breaking free. She went into the lobby and asked for help.
"She came in with a little backpack full of things as if she intended not to return and said, 'I need some help,' told the officers what took place. We immediately called the paramedics in, checked her out real quickly," said Chief Michael Holub, La Grange Police Department. "The mother was deported about four years ago. So this was the court-appointed legal guardian since that time."
After paramedics examined the girl, police went to the home to check on the girl's 9-year-old sister. She and Ochoa were sleeping. Both were taken to the police station and Ochoa was placed under arrest.
The girl said she was able to free herself four hours after being tied up by Ochoa. She told police it was not the first time that she had been tied up.
"She was bound with some electrical cord, like an extension cord, with her hands behind and also had something thrown over, I think it was a towel or a sheet, so she couldn't see," said Chief Michael Holub, La Grange Police Dept.
A former neighbor says the girls kept to themselves.
"The only thing that I really remember was that they were pretty contained at the front door and on the grass with their two little dogs. They really didn't come over and play with my children. I don't know if they were just shy or what," said the neighbor.
The sisters are now in the custody of the Illinois Department of Children and Family Services. DCFS and the Cook County State's Attorney's Office are checking for any other possible abuse by Ochoa.
La Grange police say the 11-year-old would not tell investigators why she was tied to a pole. Police say the girl learned through the DARE program at school how to get to the police department.