The sigma virus is a vertically transmitted pathogen that commonly infects natural populations of Drosophila melanogaster. This virus is the only known host-specific pathogen of D. melanogaster, and so offers a unique opportunity to study the genetics of Drosophila-viral interactions in a natural system. To elucidate the population genetic processes that operate in sigma virus populations, we collected D. melanogaster from 10 populations across three continents. We found that the sigma virus had a prevalence of 0-15% in these populations. Compared to other RNA viruses, we found that levels of viral genetic diversity are very low across Europe and North America. Based on laboratory measurements of the viral substitution rate, we estimate that most European and North American viral isolates shared a common ancestor approximately 200 years ago. We suggest two explanations for this: the first is that D. melanogaster has recently acquired the sigma virus; the second is that a single viral type has recently swept through D. melanogaster populations. Furthermore, in contrast to Drosophila populations, we find that the sigma viral populations are highly structured. This is surprising for a vertically transmitted pathogen that has a similar migration rate to its host. We suggest that the low structure in the viral populations can be explained by the smaller effective population size of the virus.