A central focus of population genetics has been examining the contribution of selective and neutral processes in shaping patterns of intraspecies diversity. In terms of selection specifically, surveys of higher organisms have shown considerable variation in the relative contributions of background selection and genetic hitchhiking in shaping the distribution of polymorphisms, although these analyses have rarely been extended to bacteria and viruses. Here, we study the evolution of a ubiquitous, viral pathogen, human cytomegalovirus (HCMV), by analysing the relationship among intraspecies diversity, interspecies divergence and rates of recombination. We show that there is a strong correlation between diversity and divergence, consistent with expectations of neutral evolution. However, after correcting for divergence, there remains a significant correlation between intraspecies diversity and recombination rates, with additional analyses suggesting that this correlation is largely due to the effects of background selection. In addition, a small number of loci, centred on long noncoding RNAs, also show evidence of selective sweeps. These data suggest that HCMV evolution is dominated by neutral mechanisms as well as background selection, expanding our understanding of linked selection to a novel class of organisms.