The woman, now 43, has filed a lawsuit alleging that the couple harassed her to try to make her take back her claims, US media report.
Petty served four-and-a-half years in prison after pleading guilty to attempted rape of the then teenager.
Last year he was arrested for failure to register as a sex offender.
In the lawsuit, filed in the US District Court for the Eastern District of New York, the woman alleges that Ms Minaj offered her $500,000 (£360,000) via an intermediary in return for recanting her accusations against Petty.
The lawsuit claims that, shortly after Petty's arrest in 2020, the intermediary gave the rapper the woman's number. Ms Minaj is alleged to have called her and offered to fly her and her family to Los Angeles if she could "help" her.
The offer was declined, the lawsuit says.
The woman also claims that she turned down Ms Minaj's offer to have her publicist draft a statement recanting the allegation.
According to the lawsuit, the woman is said to have told Ms Minaj: "I need you to know woman to woman, that this happened."
The woman further claims that within days of rejecting the offers, she and her family "suffered an onslaught of harassing calls and unsolicited visits".
The woman said she had not been able to work since May 2020 "due to severe depression, paranoia, constant moving, harassment and threats" from the celebrity couple and their associates.
The lawsuit, which seeks unspecified damages, says she is living in hiding as she fears retaliation.
The musician's legal team has not yet responded to the accusations, according to US media.
Ms Minaj and Petty began dating in 2018 and announced a year later that they were married. The couple have an 11-month-old son.