Zombies are humans who have returned from the dead due to a curse. The only one seen is Chandu (although Renfield Sr. was brought back briefly using alchemy).
The zombie Chandu was created after Count Dracula beat him in a chess match. Chandu was mummified for losing. Because Count Dracula cheated, Chandu was cursed to walk the earth as a zombie.
In "The Bodyguard", Talitha and Vlad discuss a time when they fought zombies in Haiti. Vlad apparently screamed and fainted, while Talitha held them off.
In "When You're a Stranger" when The Count catches his children talking to humans he says "Mixing with zombies I could forgive, understand even, but breathers!"