APOBEC family members play crucial roles in antiviral restriction. However, certain APOBEC3 (A3) proteins drive harmful hypermutation in humans, contributing to cancer. The cancer-associated A3 proteins are capable of transiting from the cytosol to the nucleus, where they can cause genome mutations. Here, we uncover a specific set of cellular pathways that protect genomic DNA from the major cancer-associated A3 proteins. Through genetic and proteomic screening, we identify UBR4, UBR5, and HUWE1 as key ubiquitin E3 ligases marking cancer-associated A3B and A3H-I for degradation, thereby limiting A3-driven hypermutation. Mechanistically, UBR5 and HUWE1 recognize A3s in the absence of their RNA binding partner, thus promoting proteasomal degradation of APOBEC3 protein that is not engaged in its antiviral cellular function. Depletion or mutation of the E3 ligases in cells and human cancer samples increases A3-driven genome mutagenesis. Our findings reveal that UBR4, UBR5, and HUWE1 are crucial factors in a ubiquitination cascade that maintains human genome stability.