Nielsen was nominated for the 2013 Tony Award for Best Lead Actress in a Play for her performance as Sonia in Vanya and Sonia and Masha and Spike and the 2019 Tony Award for Best Featured Actress in a Play for her performance in Gary: A Sequel to Titus Andronicus.
Her mother, a Democrat, worked in government, at one point for president Jimmy Carter, and her father was a U.S Navy captain.
She next appeared in Jackie: An American Life (1997) playing various characters, including Rose Kennedy and Marilyn Monroe.
[9] In 2005, she played Eunice Hubbell opposite Natasha Richardson's Blanche Dubois and Amy Ryan's Stella in A Streetcar Named Desire.
In 2017, she played the role of Monica Reed in the limited run of Present Laughter, along with Kevin Kline and Cobie Smulders.
Nielsen won the Obie and a Drama Desk Award nomination for Best Featured Actress[16] for her role as Mrs. Siezmagraff in Betty's Summer Vacation (1999) by Christopher Durang.
Her first Off-Broadway appearance was in a 1984 New York Shakespeare Festival production of Henry V at the Delacorte Theater in which she played Mistress Quickly.
In 2005, Nielsen starred as Veronica in Christopher Durang's play Miss Witherspoon at Playwrights Horizons.