Wright began her acting career on stage, before appearing in films like Stuart Saves His Family, Devil in the Flesh, and Shadow Hours, and television shows such as Suddenly Susan, Dangerous Minds, Frasier, Friends, Malcolm in the Middle, Ally McBeal, Girlfriends, and Judging Amy. She also had a recurring role in the Fox series Power Rangers in Space in 1998.

In 2001, Wright was cast as Laverne Roberts in the NBC comedy series, Scrubs. After six seasons, her character was killed off in "My Long Goodbye". She returned in season seven playing a new character, Nurse Shirley. Initial reports stated that her character would be the alcoholic, irreligious sister of Laverne, but these turned out to be inaccurate. She later returned to play Nurse Roberts in the season 8 finale, "My Finale", as JD is looking back on all the people in his life. In 2000s, Wright also guest starred on NYPD Blue, Cold Case, NCIS, and Mad Men. She also had supporting parts in films such as Bring It On, The Brothers, and Johnson Family Vacation.

In 2008, Wright began appearing as nurse Maxine Landis in the NBC daytime soap opera, Days of Our Lives. From 2012 to 2013, Wright also had the recurring role as Mildred Clemons in the Shonda Rhimes' series, Private Practice, and in 2015 appeared in an episode of Scandal. In 2015, she joined the cast of USA Network legal series Suits for season five, as Harvey Specter’s new secretary, Gretchen Bodinski.