Young was born as Amy Young in Asheville, North Carolina. She had to change her name to join the Screen Actors Guild since there was another Amy Young registered. Young graduated from the Asheville School in 1987, Yale University in 1991, and the British American Drama Academy at Oxford University in England.
Early in her career, Young starred in several Broadway shows including The Life and Randy Newman's Faust. In 1995 she made her television debut in the recurring role of the NBC daytime soap opera Another World as Dr. Courtney Evans. She later guest-starred in Law & Order, The Drew Carey Show and Nash Bridges, and appeared in the feature film Black and White in 1999.
Young has guest-starred in numerous television shows including The X-Files, ER, Frasier, The West Wing, NCIS, Grey's Anatomy, Private Practice, Two and a Half Men, Ghost Whisperer, Supernatural, The Mentalist and Castle. Her film credits include We Were Soldiers (2002), Larceny (2004), Mission: Impossible III (2006), Trust Me (2007), This Is Not a Test (2008) and In My Sleep (2010).
Young was a regular cast member in the USA Network series Peacemakers in 2003. The show was cancelled after one season of nine episodes. She had recurring roles in American Dreams, Scrubs, CSI: Miami and on Dirty Sexy Money as Ellen Darling, the eldest daughter-in-law of the Darling family. She also had a recurring role in Criminal Minds as Beth Clemmons from 2011 to 2012.
In 2011 Shonda Rhimes cast Young in the recurring role of First Lady Mellie Grant on the ABC political thriller television series Scandal opposite Kerry Washington and Tony Goldwyn. She appeared in every episode of the first season and was upgraded to a series regular as of season two.