The woman does not use her name and goes by Jane Roe in the lawsuit filed in Los Angeles Superior Court filed on Thursday. An email seeking comment from Brooks' publicist and attorney were not immediately answered.
The woman says in the lawsuit she had worked for Brooks' wife, country singer Trisha Yearwood, since 1999, and had started also working for Brooks in 2017.
She said the assault occurred when she travelled from Nashville to Los Angeles with Brooks, who was performing with soul singer Sam Moore at a Grammy Awards tribute to Moore in October 2019.
Brooks normally travelled with an entourage, but the two were alone on his private jet, and he booked just one hotel suite for both of them, the lawsuit says.
The woman alleges that in the suite, he appeared naked in the doorway to the bedroom and raped her.
The suit says that he then proceeded as though nothing had happened and expected her to do his hair and makeup immediately after.
She alleges that earlier in 2019, when she was at Brooks' home, he had appeared naked in front of her, grabbed her hands, and put them on his genitals.
The lawsuit says Brooks filed his own pre-emptive lawsuit in federal court in Mississippi in September, in which both he and the woman are anonymous.
In court filings in that case, the plaintiff, going by John Doe, says the allegations are "wholly untrue" and he first learned of them in July when she threatened to publicly sue him unless he gave her millions of dollars.
He asks a judge to stop the woman from "intentional infliction of emotional distress, defamation, and false light invasion of privacy".
The woman's suit also says Brooks exposed himself to her many other times and talked about sexual fantasies with her and sent her explicit text messages.
She said she was forced to keep working for Brooks because of financial hardship, which he knew about and took advantage of.
An email to the woman's attorney asking whether she had reported her allegations to police was not immediately answered.
The 62-year-old Oklahoma-born Brooks was the biggest star in country music of the 1990s, with hits including Friends in Low Places and The Thunder Rolls.