League explained that the device would have to switched off once the lights were dimmed before a movie and that this was done for piracy concerns rather than scorn towards the head-mounted device.
"But on a personal level, I advocate turning off distractions during a movie," he tweeted.
League did say that he isn't against the technology, which is currently evolving and finding its space in society. On being asked by a Twitter user if Glass users could switch off the device before the movie, League said that they would deal with that on a case-by-case basis and that it will be OK "if it is clear when they are on, clear when they are off."
The announcement follows a separate incident in January when a man using Google Glass at a theatre in Columbus, Ohio was questioned by Department of Homeland Security officials because they were concerned he was recording the film.
After the incident the Motion Picture Association of America jumped to the defense of the device saying "Google Glass is an incredible innovation in the mobile sphere, and we have seen no proof that it is currently a significant threat that could result in content theft."
Alamo Drafthouse Cinemas has theaters in Texas, Missouri, Michigan, Virginia, Colorado, New York, and California. A new Alamo Drafthouse is due to open in San Francisco later this year, which has a high concentration of Glass users and could see incidents of people using their Glass while watching movies.
Notable deaths of 2014 [PHOTOS]
Larry Ellison to step down as CEO of Oracle