Members of the apolipoprotein B mRNA editing enzyme, catalytic polypeptide-like (APOBEC) family play crucial roles as viral restriction factors, yet some APOBEC3 (A3) members drive harmful hypermutation in humans, contributing to cancer. These cancer-associated A3 members have reduced RNA-mediated retention in the cytosol, and therefore can drive nuclear DNA mutation. We show that specifically major cancer-associated members are rapidly turned-over by proteasomes, indicating the existence of cellular pathways marking cancer-associated A3s for degradation, thereby protecting cellular genomic DNA from hypermutation. Through genetic and proteomic screening UBR4, UBR5 and HUWE1 were identified as degraders of cancer-associated A3 proteins, thereby limiting A3-driven hypermutation. Mechanistically, UBR5 and HUWE1 recognize the unengaged RNA-binding interface of cancer-associated A3B and A3H-I, promoting their proteasomal degradation. Depletion or mutation of the E3 ligases in cell models and cancer samples increased A3-driven hypermutation. Our findings highlight UBR4, UBR5 and HUWE1 as crucial factors in maintaining human genome stability.