Carcinogenesis in human urothelium is driven by a high burden of mutations caused by the antiviral “APOBEC3” (apolipoprotein B mRNA editing enzyme, catalytic subunit–like 3) cytosine deaminase enzymes; however, there is no established viral etiology. BK polyomavirus (BKPyV) is a ubiquitous childhood infection that persists in the kidney during adulthood and is frequently detected in urine. Chronic BKPyV infections of normal human urothelium induced an innate response, including apical extrusion of infected cells. Local paracrine interferon signaling induced APOBEC3 expression in both infected and juxtaposed bystander cells, leading to acquisition of hallmark APOBEC3-mediated mutational signatures that recapitulated the variation in mutational character found in patients with muscle-invasive bladder cancer. In our model for urothelial carcinogenesis, uninfected bystander cells witnessing BKPyV infection become APOBEC3 damaged, escape extrusion, and acquire hypermutable advantage. “Transmutagenesis” explains how cells proximal to infected neighbors acquire cancer-initiating mutations. This hypothesis for how urothelial cancers can develop as APOBEC3 signature rich, while remaining virus-negative, suggests that a large proportion of urothelial carcinomas may be preventable by antiviral intervention.