Viruses are neither prokaryotic nor eukaryotic. Viruses are in a separate category known as obligate intracellular parasites. By themselves, viruses do not carry the biological material necessary to reproduce; they can only replicate themselves by infecting prokaryotic or eukaryotic cells.
A virus carries just enough genetic information to replicate itself inside prokaryotic or eukaryotic cells by hijacking the cell's internal reproduction mechanisms. Because viruses are smaller, simpler parasites, they often infect only a few species.
There is no known virus that can infect every animal on earth. For example, the Ebola Zaire virus is disastrous in humans, but the virus can be safely carried by its natural host, bats.