Cryptozooglogists, Necrologists, and Zombologists classify Zombies as Homo Necrosis Zombifis under the supernatural sciences. The complete paranormal classification is below:

Zombie Scientific Classification Chart

Kingdom: Cryptida (Supernatural Cryptids)
Phylum: Immortalis (Immortals)
Class: SupraNecrosis (Living Dead Beings)
Order: Magica (A Product Of Magic)
Family: Anthropophagis Sanguinus (Survives Off Human Flesh And Blood)
Genus: Homo Necrosis (The Melding Of Human And Zombie)
Species: Homo Necrosis Zombifis (Scientific Name For Zombies)

Cryptida is the seventh Kingdom that mainstream science refuses to acknowledge.

Despite Zombies being technically Immortal they also are in a state of rotting necrosis which means they will be non-animated in less than a decade depending on the circumstances of the environment they menace.  However magical intervention could theoretically extend their destructive lives indefinitely.  The original supernatural zombie virus is a product of a magical accident.  In addition to Practitioners Of Magic raising corpses from the dead, the zombies themselves can pass on the virus to make new zombies.

See also the scientific name for Vampires.