The actress will appear in an upcoming episode of the show as a museum curator called Beth, Entertainment Weekly reports.
Beth ends up meeting Hotch (Thomas Gibson) while he is training in the park.
Young has previously starred in shows including CSI: Miami, Scrubs, Dirty Sexy Money and Grey's Anatomy.
She will also appear in ABC's upcoming new drama Scandal, which comes from Grey's Anatomy creator Shonda Rhimes.
Young is expected to guest star in the same episode of Criminal Minds as Charles S Dutton, who recently signed up to play a boxing trainer.
The show airs on Wednesdays at 9/8c on CBS.