Krista Stegall said TV network CBS should have checked the criminal record of Justin Sebik, who was thrown off the show after the incident.
Mr Sebik said he was only joking when he pulled the knife on Ms Stegall while they were kissing on the show in 2001.
The lawsuit said Mr Sebik had been arrested on assault charges in 1996 and 1997, and had been aggressive towards other housemates before the incident.
"I don't think there's any doubt [CBS] made a huge mistake letting him in and keeping him in," Ms Stegall's attorney, Clayton Burgess, said.
Ms Stegall is seeking unspecified damages, the lawsuit said.
A spokeswoman for CBS said the network thought there was "no merit" in the lawsuit, and added it was prepared to defend it "vigorously".
Ms Stegall and Mr Sebik were taking part in the second series of the US Big Brother in 2001.
CBS said they had carried out a thorough check on the contestants' backgrounds beforehand.
Warning
The second series of the US Big Brother saw 12 strangers living together for the chance to win $500,000 (£355,300).
During the knife incident, Mr Sebik was heard to say: "Hang on, I'm going to slash your throat. Would you get mad if I just killed you?"
CBS producers decided to throw him out, having warned him previously about derogatory comments towards women and intimidating other contestants.
In January 2002, he was arrested after he was accused of choking a woman and breaking her ankle.