The nearly 3 orders of magnitude variation in size observed among double-stranded DNA viruses (dsDNA) has important ecological consequences, but the factors responsible for this variation remain poorly understood. Here we first evaluate if a relationship exists between the genome size of diverse dsDNA viruses and their hosts in single-celled organisms (prokaryotes and eukaryotes). We find that dsDNA genome size increases systematically, though less than proportionally, with host genome size. We next evaluate possible relationships between virus size, host size and burst size in an analysis that includes both single-celled and multicellular hosts where genome size and cell volume are not as highly correlated. Here we find that virus volume increases sublinearly with host cell volume (but not genome size) across species, and that virus burst volume (burst size * virus volume) increases with host cell volume. These findings suggest that the size and number of dsDNA viruses produced by a particular host may be constrained by the volume of the infected host cell. This may be useful for better understanding virus-host population dynamics, and ultimately, a better understanding of which viruses may infect which hosts (i.e., host specificity) and the likelihood of cross-species transmission events (i.e., host jumping).