The suit against the Karolyis and Dr. Larry Nassar was filed Thursday in Superior Court in Los Angeles County, where the plaintiff now lives. The complaint alleges the Karolyis "turned a blind-eye to Nassar's sexual abuse of children."
The lawsuit says the alleged abuse occurred at a Karolyi-run facility in Texas that also served as the training site for USA Gymnastics, also a defendant.
The civil complaint says the couple instituted a regimen of intimidation and fear that included striking, scratching gymnasts and depriving minors of food and water. A "toxic environment" gave Nassar the opportunity to commit sexual abuse, the suit claims.
The suit claims that USA Gymnastics, the governing body of the sport in the United States, ignored and/or actively concealed the abuse by the former team doctor.
The Karolyis didn't immediately respond to CNN's request for comment. Neither did attorneys for Nassar.
USA Gymnastics denied the allegations, saying when it first learned of any athlete concerns regarding Nassar, they "dismissed him from further involvement and reported those concerns to the FBI."
The lawsuit says the gymnast, who is referred to as Jane LM Doe, was part of the US national team between 2006 and 2011. The sexual abuse began when the woman was a minor, the suit alleges.
Earlier this month, the attorney general of Michigan announced he was reviewing sexual assault allegations against Nassar. Bill Schuette said his office was taking over the investigation from police at Michigan State University after a request from Chief Jim Dunlap.
A news release from Schuette
called the case "complex." It said Nassar is a former associate professor at the university.
Martha Karolyi retired from her role as national team coordinator after the US women's team dominated the competition at the recent Rio Olympics. She had held the position since 2001, after taking over for her husband.
Bela Karolyi gained famed for coaching Nadia Comaneci, the Romanian gymnast who won five total gold medals in 1976 and 1980. Karolyi coached Mary Lou Retton to a gold at the 1984 Summer Olympics in Los Angeles. His wife coached the US Olympic Team in 1996 to its famous win while Bela Karolyi inspired his pupil Kerri Strug to land the vault that helped the US to gold.
The Karolyis defected to the United States from Romania in 1981.