As is becoming increasingly common on Xbox 360, Call of Duty: Ghosts will require a hard drive installation. However, this only applies to the single-player campaign. If you plan on simply jumping into online multiplayer, you'll be able to pop in the disc and start fragging.
If you do want to play the single-player campaign, you'll need to install about 3GB of data, One of Swords reveals. That means the game will be entirely playable on a 4GB Arcade system--assuming you have nothing else installed, of course. You can also pick up an Xbox-compatible USB drive for the installation.