Troopers say they were notified on Tuesday of the alleged sexual assault that happened on September 18th.
The nine-year-old told her mother about the incident two days later, and she was interviewed by authorities on Tuesday.
Police say they learned the girl was raped at her father's home. Matthews, police say, is an acquaintance of the girl's father.
Matthews was arrested on charges of Rape, Unlawful Sexual Contact, and Endangering the Welfare of a Child.
Matthews was committed to James T. Vaughn Correctional Center in default of $56,000 secured bail.