The cancellation means that the Met will present only five new productions next season, which will be announced next month, down from six. When Mr. Gelb became general manager just over a decade ago, he decided that mounting more new productions was necessary for the company to remain artistically vibrant and to help it attract new audiences. Initially he presented seven new productions each season, up from the three or four before he arrived.

Mr. Gelb said the decision to pull the plug on “Forza” was “not a reflection upon my feeling about Calixto’s talent as a director,” and said he still hoped Mr. Bieito would work at the Met. But he said it was unclear when or if “Forza” would be staged, as future seasons have been planned through the 2020-21. Mr. Bieito did not immediately respond to a request for comment.

Mr. Bieito is the second high-profile, innovative director whose production was derailed en route to the Met. The company announced over the summer that its plans to bring Stefan Herheim’s production of Wagner’s “Die Meistersinger von Nürnberg” from the Salzburg Festival to the Met in a future season had fallen apart for a variety of reasons.

Under Mr. Gelb’s leadership the Met, which has had a reputation for mounting conservative, traditional productions, has increasingly turned to more experimental international directors, including Willy Decker and Patrice Chéreau, whose posthumous production of Strauss’ “Elektra” was a highlight last season.