“We will vigorously defend this lawsuit through the appropriate legal process. I am looking forward to being entirely vindicated and exonerated,” a statement from his lawyers said.
Mr Barnett was ranked as the world’s most powerful sports agent in 2019 by Forbes magazine.
The civil case was filed on Wednesday.
According to court documents, the pair first met in the 1990s through a professional athlete in London and reconnected online and then in person in 2017.
Within a matter of weeks she relocated to the UK with her teenage children – with sports agency CAA Stellar, headed by Mr Barnett, covering moving expenses.
The filing says that upon her arrival, he told her he “owned” her and raped her in a hotel room.
Mr Barnett went on to impose strict rules to obey him at all times, referring to him as “My Master” and to “never say it hurts”, according to the lawsuit.
The complaint goes on to describe alleged degrading acts that included drinking urine or ingesting faeces.
The alleged torture also included the woman “tied up overnight without food or water”.
She says she was “trafficked, threatened, tortured, and held” in bondage in different locations throughout the world, including Los Angeles, from 2017 to 2023.
“Realising she was powerless against a dangerous predator, Ms Doe submitted to Barnett in order to avoid being severely beaten or even killed,” the lawsuit said.