Why the zombie apocalypse?
In a fantasy world, the rise of the zombies would need to be, well, fantastic. Given the literal "dead walking the earth" thing, an event of tremendous magical magnitude seems appropriate. A super-necromancer might have finally succeded in his arcane ritual. Maybe a party of adventurers failed in their attempts to prevent it and evil has (temporarily) won. The players in this game wouldn't know about this, however. This set up wouldn't necessarily radically alter any game mechancics. It gives a BBEG to fight against, if the PC's make it that far.
Although this is beginning to remind me, a bit, of the Midnight setting for 3E, which I did not care for.
Another alternative is something more akin to the Cataclysm in the Dragonlance setting. The gods up and left, creating all sorts of havoc. The principal consequence of the abdication of the pantheon is the dead rise. Another serious consequence is the lack of any divine or clerical power. No cure spells! No turning undead! This really ramps up the survival horror aspect of such a game, as traditional means of overcoming environmental hazards, especially injury, are now gone. The denial of turn undead seems pretty harsh in an undead-centric game, but it also makes sense. This gampaign frame seems a bit more open than the one above. The PC's can try to figure out why the gods left and what, if anything, can be done to resore clerical power. Or they can loot the now vacant churches. Either way, they have plenty to do.