Mobiles may still be set on vibrate mode and people will be permitted to speak on their phones in lobbies and during intermissions. Audible pagers have also been outlawed.
Phil Reed, the Manhattan councillor who sponsored the legislation, said the idea came from theatre owners who had tired of incessant phone ringing and loud conversations during performances.
"I think it's a real quality of life issue," said Mr Reed.
"People overwhelmingly want this to happen. And because it would only apply during the performance, it's not a lot to ask of people."
The decision overrode a veto by the city's mayor, Michael Bloomberg, who argued that it would be almost impossible to enforce. "Considering the challenges facing the city, we think our law enforcement officers should spend their time keeping New Yorkers safe instead of raiding movie theatres," said a spokesman for the mayor.
Mobile phone company representatives also opposed the ban. "We just feel like you can't legislate common sense," said Kimberly Kuo of the Cellular Telecommunications and Internet Association.