Filmmaker Woody Allen sued Amazon Studios, claiming breach of contract for refusing to distribute his most recent movie, “A Rainy Day in New York,” and terminating a four-picture production and distribution deal without cause.

In a suit filed Thursday in federal court in the Southern District of New York seeking more than $68 million in damages, Mr. Allen said Amazon backed out of his deal last June after an old accusation that the director and actor had molested his adopted daughter, Dylan Farrow, in 1992 resurfaced as the #MeToo movement was gathering steam.

“Amazon has tried to excuse its action by referencing a 25-year-old baseless allegation against Mr. Allen, but that allegation was already well-known to Amazon (and the public) before Amazon entered into four separate deals with Mr. Allen—and in any event, it does not provide a basis for Amazon to terminate the contract,” the suit said.

In recent years, Ms. Farrow has become more vocal about her accusation against Mr. Allen and in a 2014 New York Times piece criticized those who have worked with him.

Since her column and a 2018 television interview with Ms. Farrow on “CBS This Morning” detailing the allegation, some actors and actresses have publicly expressed remorse about appearing in Mr. Allen’s movies.