Viruses interact with hundreds to thousands of proteins in mammals, yet adaptation against viruses has only been studied in a few proteins specialized in antiviral defense. Whether adaptation to viruses typically involves only specialized antiviral proteins or affects a broad array of proteins is unknown. Here, we analyze adaptation in ~1,300 virus-interacting proteins manually curated from a set of 9,900 proteins conserved across mammals. We show that viruses (i) use the more evolutionarily constrained proteins from the cellular functions they hijack and that (ii) despite this high constraint, virus-interacting proteins account for a high proportion of all protein adaptation in humans and other mammals. Adaptation is elevated in virus-interacting proteins across all functional categories, including both immune and non-immune functions. Our results demonstrate that viruses are one of the most dominant drivers of evolutionary change across mammalian and human proteomes.