Censors in the world's most populous Muslim-majority country said they decided to ban the film, which had been set for release Friday, as the depiction of prophets is forbidden under Islamic law.
As well as being a biblical figure, Noah is also a prophet for Muslims.
"We rejected the screening of the film in Indonesia," Zainut Tauhid Saadi, a member of the Indonesian Censorship Board, told AFP.
"The visual depiction of a prophet is forbidden in Islam," he said, adding: "The film will hurt both Christian and Muslim communities."
It came after the Paramount film based on the story of Noah's ark, which stars Crowe as Noah and is directed by Darren Aronofsky, was banned by Qatar, Bahrain and the United Arab Emirates earlier this month.
AFP