You've made one of the classic mistakes: You should never consider anything produced by Hollywood to be in any way a reflection on reality (other than whatever they put in front of an actual, not virtual, camera, and even then you have to be wary). As described in the movie, it has been some years since the moon was shattered.
Yes, it would be possible (with the application of a great deal of force) to shatter the moon in a manner similar to this such that this one frame would be valid. However, to do simply that would result in the pieces either spreading out across the solar system if the pieces were imparted sufficient velocity to escape the moon's gravity, otherwise they would collapse back into an effectively spherical volume again. This frame would only be valid a short time after the moon's shattering, and not after the time period that the movie implies has passed. In actuality, the chunks would variously hit the earth, form a ring around the earth, escape the earth/moon's gravity altogether, and anything that didn't escape would eventually re-coalesce.
A second possibility is that in the shattering of the moon, the moon's angular momentum was increased prior to its disassembly, so that the pieces are orbiting one-another, however, if I recall correctly, the image of the moon in the movie is more-or-less static. However, some of the pieces depicted are very large, they should already be re-forming themselves into smaller spheres. At this scale, under even the moon's lower gravity, solid matter will behave as if it was fluid.
To actually have a fractured moon orbiting your planet like this, without collapsing, you'd need a huge, pretty implausible (unless you're in a very high-tech sci-fi environment) anti-gravity unit at the centre, keeping everything where it is in a very delicate balance of forces.
For this picture to be valid in isolation, the timeframe we're talking about would be less than an hour, and probably a matter of minutes. However, in the context of the movie, it is not valid at all.