If you would like details on the viral family, please see parvoviridae, as this node is more about nomenclature and specifically, the etymology of the word parvovirus. Thanks to belgand for pointing this out.

parvo comes from the Latin "parvus" which means small, and virus comes from the Latin "virus" which means poison.

The Oxford English Dictionary cites a usage of "virus" from 1527 to mean the venom from a poisonous animal. Apparently, Edward Jenner, and later Louis Pasteur used it to indicate a biological agent that was able to move from one infected person to another. Modern usage has restricted it to non-cellular organisms that reproduce in the cells of other organisms using the cellular machinery of the host cells.

The origination of the combination of "parvo" and "virus" is difficult to find. I suspect that a medical researcher who discovers or decides that some distinction ought to be made (such as the distinction between the generic idea of a virus and the idea of one that is composed of a single strand of DNA and has no envelope) might coin a term such as parvoviridae. Then, either the term will spread (like a virus - let's say a meme), or it will be challenged by one or more terms that others came up with for the same purpose or one very similar. Of course, the researchers involved may now generally be institutions like the American Medical Association or the World Health Organization.