While nowhere near the install size requirements of Battlefield 3 (that game requires a whopping 15.5 gigs total), Call of Duty: Modern Warfare 3 still demands quite a hefty chunk of your hard drive. If you have a 4GB Xbox, don’t even bother trying to install Modern Warfare 3.
In order to install MW3, your Xbox must have a minimum of 7.45GB free. Now keep in mind that this is completely optional; you can still play the game without installing, you just won’t get the optimum Modern Warfare experience.

Posted: Nov 03, 2011 10:51 am

Source: http://www.justpushstart.com/2011/11/03/modern-warfare-3-install-size-for-xbox-360-confirmed/