The lawsuit, filed in federal court, identifies the victim only as H.T., Courthouse News Service reported Wednesday.
It says the rapist, Jamie Melendez, who was 20 when the victim was raped, was sentenced to 16 years probation.
"Conditions of probation include an order that he initiate proceedings in family court and comply with that court's orders until the child reaches adulthood," the plaintiff says in court papers. "The plaintiff here seeks to enjoin enforcement of so much of the state court's order as violates her federal rights by binding her to an unwanted 16-year legal relationship with her rapist."
H.T. says Melendez was ordered to pay $110 a week in child support and then, in 2012, went to court seeking visitation. He offered to withdraw his request if the order for child support was voided.
In legal documents, H.T. says both she and her mother told the court they wanted no contact with Melendez. She said they wanted payments to be treated as court-ordered restitution and not as child support.
H.T. said she has been put in a position where she cannot ignore the family court proceedings because she faces sanctions, including possible loss of custody of the child, if she fails to comply.