IDOC says Stephanie Klein was hired on October 18, 2010 and resigned on May 11 of this year.
Officials say she taught at the minimum security South Idaho Correctional Institution south of Boise before being assigned to the South Boise Women's Correctional Center.
The Ada County Sheriff's Office says Klein had sexual contact, but not intercourse, with a male inmate on 2-3 occasions between late 2010 and late 2011.
The sheriff's office says Klein disclosed the sexual contact to a supervisor earlier this year, which prompted the investigation.
IDOC says because it is a personnel matter, they will have no further comment.
Sexual contact with an inmate is a felony categorized in Idaho Code as rape and punishable by up to life prison.