The suit also accused Dylan, who turned 80 in May, of physically threatening the girl.
The alleged abuse took place at the apartment Dylan owned in New York's famous Chelsea Hotel, according to the lawsuit.
A spokesperson for Dylan, whose real name is Robert Zimmerman, said "the 56-year-old claim is untrue and will be vigorously defended."
The accuser, who now lives in Greenwich, Connecticut, says Dylan caused her "severe psychological damage and emotional trauma." She is seeking unspecified damages.
The lawsuit was filed a day before the window for filing claims under New York State's Child Victims Act closed.
The act allowed victims of abuse to sue their alleged attackers irrespective of the age of the claims or whether the statute of limitations had passed.
Last week, an accuser of late US financier Jeffrey Epstein used the act to sue Queen Elizabeth II's second son, Prince Andrew, for alleged sexual abuse.
Dylan is widely considered to be the greatest singer-songwriter of all time. His most notable works include "Blowin' In The Wind," "The Times They Are a-Changin'," and "Like A Rolling Stone."
He burst onto the folk scene in New York in the early 1960s and has sold more than 125 million records around the world.
In 2016, Dylan won the Nobel Prize for Literature "for having created new poetic expressions within the great American song tradition."
Last year he released his 39th studio album, "Rough and Rowdy Ways," 58 years after the release of his first.