In RNA viruses, mutations occur fast and have large fitness effects. While this affords remarkable adaptability, it can also endanger viral survival due to the accumulation of deleterious mutations. How RNA viruses reconcile these two opposed facets of mutation is still unknown. Here we show that, in human immunodeficiency virus (HIV-1), spontaneous mutations are not randomly located along the viral genome. We find that the viral mutation rate experiences a threefold reduction in the region encoding the most external domains of the viral envelope, which are strongly targeted by neutralizing antibodies. This contrasts with the hypermutation mechanisms deployed by other, more slowly mutating pathogens such as DNA viruses and bacteria, in response to immune pressure. We show that downregulation of the mutation rate in HIV-1 is exerted by the template RNA through changes in sequence context and secondary structure, which control the activity of apolipoprotein B mRNA-editing enzyme catalytic polypeptide-like 3 (A3)-mediated cytidine deamination and the fidelity of the viral reverse transcriptase.