I don't think so, i mean unless the zombie has kryptonite teeth
Probably all the other super hearoes could, have ya read dc comics series Blackest Night?
Just about all the super heroes and villains turn into zombies due to the Black Lantern ring till the end of the series
So maybe other zombiefied heroes or villains could zombify him(could, probably not cause he is the man of steel)
Just like Marvel comics Marvel Zombies, all the superhumans litterely get zombify and eat up the human race near extinction, and also the entire universe!