The lawsuit claims she was left with "emotional pain, suffering, and a loss of enjoyment and life".
Cuba's lawyer Mark Heller says the actor denies the allegation and insists the incident never took place.
He said: "The allegations are false. It's an event that took place seven years ago.
"No complaint was ever lodged. We believe the allegations and the complaint will be dismissed.
"My client is totally innocent of any of these false allegations and we're confident it will be dismissed.
"She's probably just somebody who's looking for some glory to bask in the publicity and notoriety of Cuba Gooding Jr.'s case."
Last week, the 'Jerry Maguire' star appeared in Manhattan state court and pleaded not guilty to six other misdemeanour charges of sexual abuse and forcible touching.
A woman previously claimed he allegedly "rubbed his groin and pelvis against her buttocks while simultaneously grabbed her buttocks and breast with her hand" in 2001.
And last year, Cuba - who has denied all charges" - was accused of groping three women in 2018, and "grabbing a woman's buttocks and breast and forcibly kissing her, inserting his tongue into her mouth".
In December 2019, his lawyer said: "Unfortunately, people come out of the woodwork, making false allegations against Cuba, as oftentimes happens when a celebrity is accused by the District Attorney's Office in a Public Forum.
"The spurious, uncharged allegations offered by the District Attorney's Office are so ancient and outdated and lacking in details and impairs the Defendant from defending against them; thus, it demonstrates that the District Attorney's Office's motive in introducing these inflammatory, uncharged allegations is not for any probative value, but to merely gain an advantage against the Defendant and prejudice the Jury against the Defendant."
Sexual harm - Do you need help?
If it's an emergency and you feel that you or someone else is at risk, call 111.
If you've ever experienced sexual assault or abuse and need to talk to someone contact the Safe to Talk confidential crisis helpline:
• Text 4334 and they will respond.
• Email support@safetotalk.nz
• Visit https://safetotalk.nz/contact-us/ for an online chat
Alternatively contact your local police station.
If you have been abused, remember it's not your fault.