Julie Taymor's attorneys said in a statement Tuesday that "the producers' actions have left her no choice but to resort to legal recourse to protect her rights."
Taymor is asking for a minimum of $1 million.
Lead producers Michael Cohl and Jeremiah J. Harris disputed the allegations, saying in a statement that "the production has indeed compensated Ms. Taymor for her contribution as a co-book writer."
Taymor was fired in March from the $75 million musical, which has gone through problems, such as delays and accidents.
But this isn't the only legal issue for producers, the Stage Directors and Choreographers Society earlier filed an arbitration claim against them over royalties.
The Associated Press contributed to this report.