Kennedy began her acting career on the stage, with the Marian Street Theatre, Killara, appearing in The Trojan Woman and Macbeth.
Starting in the 1970s she also acted in various television roles, with appearances in Certain Women, Silent Number, Wayzgoose, Doctor Down Under, The Restless Years, Bellamy, and 1915.
She continued to play supporting roles in feature films, including I Can't Get Started (1985), The Empty Beach (1985), Death in Brunswick (1991), The Sum of Us (1994), Idiot Box (1996), Thank God He Met Lizzie (1997), My Mother Frank (2000), Matter of Life (2001), and Swimming Upstream (2003).
Starting 2006, Kennedy appeared in a recurring role in the soap opera Neighbours as Mishka Schneiderova, Lou Carpenter's Russian partner whom he met online.
Since 2013 Kennedy has been a regular cast member in the Australian period drama A Place to Call Home playing the role of Inverness local gossip who means well, Doris Collins.