Olsen was born in Sherman Oaks, California, to Jarnette "Jarnie", a personal manager, and David "Dave" Olsen, a real estate developer and mortgage banker. She is the younger sister of twins Mary-Kate and Ashley Olsen, who became noted at an early age as TV and film stars. Olsen also has an older brother, Trent, and two younger half-siblings. In 1996, Olsen's parents divorced. The Olsens have Norwegian ancestry on their father's side and English ancestry on their mother's side.

After graduation, she enrolled at New York University's Tisch School of the Arts. In 2009, Olsen spent a semester studying in Moscow at the Moscow Art Theatre School through the MATS program at the Eugene O'Neill Theater Center.

Olsen began acting when she was four years old and co-starred in six of Mary-Kate and Ashley's productions; she also auditioned for the film Spy Kids. She almost quit acting in 2004 due to the media frenzy surrounding Mary-Kate's eating disorder. Olsen's breakout role came in 2011, in the film Martha Marcy May Marlene. The film, along with Olsen's performance, received critical acclaim. Olsen was nominated for and won numerous critics awards for her portrayal of the titular character Martha, a girl suffering from delusions and paranoia after fleeing her life in a cult and returning to her family. She next appeared in the horror film remake Silent House, in which she played the role of Sarah. The film received mixed reviews, but Olsen's performance was praised. Olsen also appeared in the music video "The Queen" by Carlotta. Olsen filmed the movie Red Lights in mid-2011, and it was released in the U.S. on July 13, 2012. She starred in Josh Radnor's film Liberal Arts, which was released on January 22, 2012. She and Dakota Fanning starred in Very Good Girls, a 2013 release.

Olsen attended New York University's Tisch School of the Arts and the Atlantic Theater Company and graduated in March 2013 after six years of intermittent study. Her sisters' clothing line "Elizabeth and James" was named after her and her older brother.

In September 2014, it was announced that Olsen would portray Audrey Williams, Hank Williams's wife, manager, and duet partner in the upcoming 2015 biopic film I Saw the Light directed by Marc Abraham and starring Tom Hiddleston as Hank Williams.

In January 2016, it was announced that Olsen would star alongside her Avengers: Age of Ultron co-star Jeremy Renner in Taylor Sheridan's directorial feature film debut, Wind River. In August 2016, it was announced that she would star in Matt Spicer's Ingrid Goes West opposite Aubrey Plaza. Both films were released in August 2017.