The Swedish actress, who gained fame in the original “The Girl With the Dragon Tattoo” series, plays seven sisters in her new film.

Before filming started, actress Noomi Rapace worried that her next role would be a “suicide mission.” In “What Happened to Monday?”, a Netflix film that debuts in mid-August, Ms. Rapace stars as a set of septuplets in hiding from a government that brutally enforces a one-child policy due to overpopulation. Each of the seven sisters has a very different personality, and for scenes in which they interact, Ms. Rapace filmed alongside a body double or in front of a green screen with tennis balls marking the places of her siblings. Ms. Rapace, 37, is best known for playing Lisbeth Salander, the antisocial computer-hacker heroine in the original Swedish-language “Girl With the Dragon Tattoo” film series (2009), based on Stieg Larsson’s books. After that performance, she quickly learned to speak English and went on to star in Hollywood films, including “Sherlock Holmes: A Game of Shadows” (2011) and “Prometheus” (2012). In “What Happened to Monday?”, set in a dystopian future, the sisters are named for days of the week and can only leave their house on that day. Outside their apartment, they must all pretend to be the same person. After the sister named Monday disappears, the others try to figure out what happened to her. “They feel like they’re all me at different times of my life,” says Ms. Rapace. “I have all the aggression, the dream, the innocence, the shyness—I have it all in me.” The sister named Wednesday, for example, is athletic and energetic. The role reminded Ms. Rapace of her early teenage years, when she first became interested in martial arts.

Born Noomi Norén, Ms. Rapace grew up in both Sweden and Iceland. Her mother was a theater teacher, and her stepfather was a farmer. She has met her biological father, a Spanish flamenco singer, only a few times. At age 7, she acted as an extra on the set of an Icelandic Viking film. “I didn’t want to go home,” she remembers. “I was covered in dirt, hanging with the horses, and I didn’t want to take my costume off.” After that, she became obsessed with acting and grew determined to leave her parents’ farm. “I always had this really strong feeling of, ‘I’m going to get out. This is not my life,’ ” she says. In her midteens, Ms. Rapace fell in with a rowdy crowd and started drinking. She based the character of the sister named Thursday on those years. “I was very angry and rebellious,” she says.

Ms. Rapace soon realized she needed to get sober. “I’ve always been strong-minded, and when I decide to do something, I decide to do it,” she says. She stopped drinking and moved to Stockholm to go to college. That period inspired the character of the sister named Monday. “I straightened up, and then I became so dedicated to college,” she says. She used that same discipline to dramatically improve her English in a short time. On her world-wide publicity tour for “The Girl With the Dragon Tattoo” in 2009, she had trouble understanding reporters’ questions, and “that was my first wake-up call,” she says. She started immersing herself in English films and shows. Ms. Rapace met her former husband, Swedish actor Ola Norell, in her early 20s. When they married, they both changed their names to Rapace, French for bird of prey. They soon had a son. That period—taking care of her son as well as some of her other family members—inspired the character of Sunday, a caretaker who loses her identity in service to others.

These days, she considers herself most like the bubbly, vivacious sister named Saturday. “People think I’m this very serious [person], more like Lisbeth Salander,” she says. “But I love to dress up, and I have wig parties in my house where everybody’s having a laugh and being so stupid.” She was a long shot for the role as Lisbeth. When she first auditioned, the director told her she was too pretty for the part. She said she would cut her hair and pierce her nose and eyebrow. “I am Lisbeth Salander!” she told him. Ms. Rapace is now preparing to play a bodyguard in the coming thriller “Close.” Her training regimen includes cardio in the morning and Pilates or a barre class in the evening, as well as martial-arts practice. In “What Happened to Monday?”, her characters fight security agents and SWAT teams. To prepare, she woke up each day at 4 a.m. and spent an hour with a personal trainer before heading to the studio at 6 a.m. When she returned to her hotel at 8 p.m., she spent an hour on the treadmill. For five months, she ate small meals every three hours and had a protein shake for dinner. “I can become really skinny or…stronger, more muscular,” she says. “I’m kind of ready to go to go pretty far to find the person I’m going to play.” For the past month, Ms. Rapace has been home in London, where she lives with her teenage son. She moved there in 2011 after her divorce from Mr. Rapace. She isn’t home much, though; she’s often moving from one film set to another. “My dad was a gypsy, and I think I have that in my blood,” she says. “I love moving around.”

She has several films coming out soon: She will appear in “Unlocked,” an action movie with Orlando Bloom, and “Bright,” a fantasy co-starring Will Smith, both out later this year. “Stockholm,” a crime drama with Ethan Hawke, is scheduled to open in early 2018. Her success over the past decade still surprises her, she says. “There was a time in my life when I thought, ‘I’m not going to be alive when I’m 25.’ ”