More than 80 people died when a French-Tunisian man, Mohamed Lahouaiej-Bouhlel, drove a lorry into celebrating crowds on Thursday evening.
Elba's film, which involves a terrorist plot to bomb Paris, was released in France on Wednesday.
Game Of Thrones actor Richard Madden also appears in the movie.
StudioCanal pulled adverts for Bastille Day a day after the attack and have now asked cinemas to stop showing it altogether, according to Variety.
It's not the first time this particular film's release has been affected by attacks like the one in Nice.