Co-divergence between host and parasites suggests that evolutionary processes act across similar spatial and temporal scales. Although there has been considerable work on the extent and correlates of co-divergence of RNA viruses and their mammalian hosts, relatively little is known about the extent to which virus evolution is determined by the phylogeographic history of host species. To test hypotheses related to co-divergence across a variety of spatial and temporal scales, we explored phylogenetic signatures in Andes virus (ANDV) sampled from Chile and its host rodent, Oligoryzomys longicaudatus. ANDV showed strong spatial subdivision, a phylogeographic pattern also recovered in the host using both spatial and genealogical approaches, and despite incomplete lineage sorting. Lineage structure in the virus seemed to be a response to current population dynamics in the host at the spatial scale of ecoregions. However, finer scale analyses revealed contrasting patterns of genetic structure across a latitudinal gradient. As predicted by their higher substitution rates, ANDV showed greater genealogical resolution than the rodent, with topological congruence influenced by the degree of lineage sorting within the host. However, despite these major differences in evolutionary dynamics, the geographic structure of host and virus converged across large spatial scales.