The Oscar-winning actor is alleged to have assaulted the unnamed woman in a New York hotel room in 2013.
A legal representative for Mr Gooding, Mark Jay Heller, said the allegations were untrue.
The actor has previously faced claims that he groped several women, but this is the first time he has been accused of rape.
The woman, identified only as Jane Doe, said she met Gooding in a Manhattan bar in August 2013 and was invited to join him for drinks at a nearby hotel.
The actor said he needed to change his clothes, and invited her up to his hotel room.
The lawsuit alleges Mr Gooding then raped her. She is seeking a jury trial as well as compensatory and punitive damages.
Mr Heller told The New York Times the allegations in the lawsuit were “completely false and defamatory”.
He also noted the allegations had not resulted in criminal charges over the past seven years.
The allegation comes a year after the actor pleaded not guilty in New York to charges of groping three different women in nightclubs in the city.
Those criminal cases have yet to be resolved. Mr Gooding’s trial was due to start in April but was delayed as a result of the coronavirus pandemic.
Earlier this month, Mr Gooding attended a pre-trial hearing in New York and wore a Black Lives Matter facemask in the court room.
Mr Gooding, 52, won a best supporting actor Oscar in 1997 for the film Jerry Maguire and is known for roles in films including A Few Good Men and The Butler.
In 2016, he was nominated for an Emmy Award for his leading performance in the TV miniseries The People v. OJ Simpson.
Two years later, he starred as Billy Flynn in a West End production of Chicago