Feldshuh is of Jewish heritage, the daughter of Lillian née Kaplan and Sidney Feldshuh, who was a lawyer. Her brother David Feldshuh is the Pulitzer Prize–nominated playwright of Miss Evers' Boys. She was raised in Scarsdale, New York, in Westchester County, and graduated from Sarah Lawrence College. In her high-school years, she was a student at the National Music Camp later named the Interlochen Arts Camp as a star in their drama class. She studied acting at HB Studio in New York City. She started her career under theater director Michael Langham at the Guthrie Theater, where she was awarded the McKnight Fellowship in Acting

After graduating from Sarah Lawrence College in New York, she began performing professionally at the famous Guthrie Theater in Minnesota.

Born Terri Sue Feldshuh, she first performed under the stage name of Terri Fairchild. Later, she decided to use her Hebrew name, Tovah, as her theatrical name.

She was born to a Jewish family in New York. She married Andrew Harris Levy in 1977 and subsequently gave birth to two children.