Oh was born to Korean immigrant parents in the Ottawa suburb of Nepean, Ontario, where she attended Sir Robert Borden High School and founded the Environmental Club there. She became a ballet dancer and later became interested in acting while in high school, where she took drama classes, acted in school plays, and was a member of the drama club and took part in the Improv Games. Oh eventually studied drama at the National Theatre School in Montreal, whereafter she starred in a London, Ontario stage production of David Mamet's Oleanna.

Around the same time, she won roles in biographical TV films of two significant female Chinese-Canadians: as Vancouver author Evelyn Lau in The Diary of Evelyn Lau (Oh won the role over more than 1,000 others who auditioned); and as Adrienne Clarkson in a CBC bio-pic of Clarkson's life.

Oh is known in Canada for her lead performances in the Canadian film Double Happiness, for which she won the Genie Award for Best Actress. Her other Canadian films include Long Life, Happiness and Prosperity and Last Night, for which she again won a Best Actress Genie. Oh also won FIPA d'Or Best Actress at Cannes Film Festival for her role in The Diary of Evelyn Lau.

Oh is most familiar to American audiences from her roles in the popular films Under the Tuscan Sun and Sideways. On American television, she is renowned for her current role in the hit ABC medical series Grey's Anatomy, for which she has won both a 2006 Golden Globe Award for Best Supporting Actress in a Series and a 2005 Screen Actors Guild Award for Outstanding Performance by a Female Actor in a Drama Series. In July 2006, she received her second Emmy nomination for her work on the series.

She had also made several guest appearances on the series Popular (1999) playing a humanities teacher.

In theatre, Oh has also starred in the world premieres of Jessica Hagedorn's Dogeaters at the La Jolla Playhouse and Diana Son's Stop Kiss at Joseph Papp's Public Theatre in New York City.

In 2006, she costarred in the film The Night Listener as "Anna," alongside Robin Williams and Toni Collette. Although Oh remains active in feature film, the critically acclaimed Grey's Anatomy remains her primary, current occupation.

Oh and American filmmaker Alexander Payne were in a relationship for five years, including two years of marriage. In March 2005, the couple's spokesperson announced their separation. A month later, Oh filed for divorce.