The suit also accused Dylan, who turned 81 in May, of physically threatening the girl.
At the time a spokesperson for Dylan, who was born Robert Zimmerman, had dubbed the accusation "untrue."
In a letter Dylan's legal team filed with the federal court on Wednesday, they accused the plaintiff of deleting important text messages, and suggested that "monetary sanctions" were necessary.
On Thursday Dylan's lawyers said the plaintiff had dropped the case. Lawyers for the plaintiff did not immediately respond to an AFP request for comment.
"This case is over," said Dylan's lead counsel, Orin Snyder, in a statement given to AFP. "It is outrageous that it was ever brought in the first place. We are pleased that the plaintiff has dropped this lawyer-driven sham and that the case has been dismissed with prejudice."
The plaintiff's lawsuit was filed last summer, 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.