Malay Muslims make up about 60 percent of Malaysia's 30 million people, and Christians about 9 percent.
In the world's most populous Muslim nation, the head of Indonesia's censor board Muchlis Paeni said the plot of the film directed by Darren Aronofsky contradicted both the Quran and the Bible.
"We have to reject Noah to be screened here," Paeni said. "We don't want a film that could provoke controversies and negative reactions."
The Indonesian Council of Ulama, the country's most influential Islamic body, welcomed the move, saying films that could corrupt religious teachings should be outlawed. Many Indonesians condemned the ban on social media.
"The decision was very regrettable, so sad," filmmaker Joko Anwar said on Twitter, warning it was a backward step for Indonesia.
Much of the Muslim world, including the UAE, Qatar and Bahrain, has already banned the film, which is a box-office hit in the U.S. Some Christian conservatives also have complained of its inaccurate portrayal of the biblical account of the flood.
Paramount Pictures added a disclaimer to its marketing material, saying "artistic license has been taken" in telling the story.
The Quran mentions only 25 prophets by name, including Noah. Muslims believe that Noah, who is referred to in Arabic as Nuh, built his ark after God charged him to do it as people in his community refused to worship God alone. While there are differences between the biblical and Quranic story of Noah, both mention a terrible flood and Noah's vessel saving a pair of each species of animal.