The Parenthood actress will feature in NBC's new comedy, which stars Matthew Perry as a sportscaster who joins a support group as he tries to address the death of his wife.
Graham will play a college friend and former co-worker of Ryan King (Perry), according to Entertainment Weekly.
However, it is currently unclear when the episode starring them both will air.
Former Friends actor Perry was reported to be dating the Gilmore Girls star in 2002, and again in 2008.
Go On premiered in full on September 11, after a special preview episode aired in August during the London 2012 Olympics.
It now airs on Tuesdays at 9/8c on NBC.