Rapace's was born 28 December 1979 in Hudiksvall, her parents were Nina Norén, a Swedish actress, and Rogelio Durán, a Spanish cantador (Flamenco singer) from Badajoz. Rapace has said that she saw her father only occasionally before his death in 2007. At the age of five, she moved from Sweden to Flúðir, Iceland with her mother and stepfather.
At the age of seven, Rapace was given a non-speaking part in the film Í skugga hrafnsins by Hrafn Gunnlaugsson. This experience made her decide to be an actress. She left home at age 15 and enrolled in a Stockholm theater school.  In 1996, she made her TV debut playing the part of Lucinda Gonzales in the TV series Tre kronor. From 1998 to 1999, Rapace studied at Skara Skolscen. She has been engaged at Theater Plaza 2000–2001, Orionteatern 2001, Teater Galeasen 2002, Stockholms stadsteater in 2003 as well as at the Royal Dramatic Theatre. She drew acclaim for her award-winning portrayal of a troubled teen mother in the 2007 Danish film Daisy Diamond.
Rapace is married to Swedish actor Ola Rapace. They have a son, Lev. Her sister, Særún Norén, is a photographer.
- In the Shadow of the Raven (1988)
- Daisy Diamond (2007)
- Men Who Hate Women (The Girl with the Dragon Tattoo) (2009)
- The Girl Who Played with Fire (2009)
- The Girl Who Kicked the Hornets' Nest (2009)
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