Innes was introduced to professional theater by her father, who frequently took the family to the Stratford Festival of Canada in Stratford, Ontario. Following his advice to "do what you love", she attended Northwestern University where she was a member of the Alpha Chi Omega sorority and earned a degree in theater.

Her first stage credits were in Chicago at the renowned Goodman Theatre, where among other roles she played Stella opposite John Malkovich's Stanley in A Streetcar Named Desire. Other major stage credits include Two Shakespearean Actors with Eric Stoltz at Lincoln Center, Our Town at the Seattle Repertory Theatre, and Three Sisters at the La Jolla Playhouse in San Diego.

In 1986, Innes played the young daughter of Jerry Stiller and Anne Meara in the short-lived television sitcom The Stiller and Meara Show, but the series was canceled within a few weeks. In the 1990s, Innes guest-starred on television series such as Party of Five, My So-Called Life, and Brookl