The 83-year-old is seeking more than $68m (£52m) in damages, alleging the company backed out of a multi-picture deal without cause.
Amazon released two of Allen’s films and also distributed his TV series, Crisis in Six Scenes.
But it dropped his most recent movie, A Rainy Day in New York. According to a lawsuit filed on Thursday in New York, Allen claims Amazon backed out of the deal in June 2018 because of an old accusation that the director had molested his adopted daughter Dylan Farrow in 1992.
A Rainy Day in New York was shot in 2017 with a cast including Jude Law, Rebecca Hall, Selena Gomez and Timothée Chalamet.