Chromosome segregation during mitosis is highly regulated to ensure production of genetically identical progeny. Recurrent mitotic errors cause chromosomal instability (CIN), a hallmark of tumors. The E6 and E7 oncoproteins of high-risk human papillomavirus (HPV), which causes cervical, anal, and head and neck cancers (HNC), cause mitotic defects consistent with CIN in models of anogenital cancers, but this has not been studied in the context of HNC. Here, we show that HPV16 induces a specific type of CIN in patient HNC tumors, patient-derived xenografts, and cell lines, which is due to defects in chromosome congression. These defects are specifically induced by the HPV16 oncogene E6 rather than E7. We show that HPV16 E6 expression causes degradation of the mitotic kinesin CENP-E, whose depletion produces chromosomes that are chronically misaligned near spindle poles (polar chromosomes) and fail to congress. Though the canonical oncogenic role of E6 is the degradation of the tumor suppressor p53, CENP-E degradation and polar chromosomes occur independently of p53. Instead, E6 directs CENP-E degradation in a proteasome-dependent manner via the E6-associated ubiquitin protein ligase E6AP/UBE3A. This study reveals a mechanism by which HPV induces CIN, which may impact HPV-mediated tumor initiation, progression, and therapeutic response.