Not in the Hollywood way, no. Reanimating a dead person without an energy source (which any kind of zombie virus, let alone supernatural infection) is a violation of the laws of physics. There are, however, diseases that can cause people to engage in behavior that causes those diseases to spread - rabies, for example, is transmitted by bite, causes its victims to be insanely aggressive and thus likely to bite others, and is often fatal. Rabies of course has a vaccine, doesn't affect everybody equally, isn't always lethal, and many other things that make it unlike the classic Hollywood "zombie virus".