Zombie Morph is one of the Cosmetic features on Minecraft Central. It was added in 1st April 2016 and belongs to the category Lobby Morphs. It only works in the Lobbies. While you are morphed, there is a text in the toolbar saying "You are currently morphed as a Zombie."
The only way to obtain this feature is by purchasing a donator rank, Diamond rank or higher. The morph can be enabled in Lobbies through the Cosmetic Menu.