Technically, there is no "zombies" in Shadowrun. But we do have 2 types of critters that may fit your bill.
The first and the closest to what you want are Feral Ghouls. Feral Ghouls are Ghouls whose mind has "gone" and they have succumbed to the most base animal instincts. And, they are infectious with a simple scratch, condemning those they infect to ghoulification through HMHVV...
The second are the Shedim, Spirits from another metaplane that have to find a host before they fade to nothing... Sadly, their preferred hosts are metahuman bodies.... which gives them a "walking dead" vibe. However, they are not infectious - other then wanting to kill all living things by ripping them apart...
Ghouls are covered in the CRB 404
Shedim are page 93 of Street grimore