It could be other events (supervolcano eruption for example), but a nuclear holocaust would be similar if not too many bombs are used.
Nuclear war doesn't do much.
I think a meteor or supervolcano is also impossible from the scenes in the film, not having lots of things growing within a month doesn't fit really, but it'd be an interesting discussion.
Obviously this is why it's not mentioned, so people don't get wrapped up in the details about how it happen but the story.
The premise revolved around there being no copies of probably the most printed book on the planet, yet there other books. Even a collective, whose mission is to find all the books and knowledge it can (someone read Asimov), can't find a bible. They found a Torah, but couldn't find a bible.
Awful film.
Movie's still not great, but there are reasons they don't find Bibles :)