Zombie Game with Paddle Weapon: Dead Island: Riptide's Purna & 'Paddle of Fury'

You're likely thinking of Dead Island: Riptide.

Playable character Purna wields a unique weapon: the "Paddle of Fury"—a large, spiked wooden paddle. It's a special item found in a hidden area, not readily available.

Let me know if this matches your memory!