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.
