HIV-1 sequence diversity presents a major challenge for the clinical development of broadly neutralizing antibodies (bNAbs) for both therapy and prevention. Sequence variation in critical bNAb epitopes has been observed in most HIV-1–infected individuals and can lead to viral escape after bNAb monotherapy in humans. We show that viral sequence diversity can limit both the therapeutic and prophylactic efficacy of bNAbs in rhesus monkeys. We first demonstrate that monotherapy with the V3 glycan-dependent antibody 10-1074, but not PGT121, results in rapid selection of preexisting viral variants containing N332/S334 escape mutations and loss of therapeutic efficacy in simian-HIV (SHIV)–SF162P3–infected rhesus monkeys. We then show that the V3 glycan-dependent antibody PGT121 alone and the V2 glycan-dependent antibody PGDM1400 alone both fail to protect against a mixed challenge with SHIV-SF162P3 and SHIV-325c. In contrast, the combination of both bNAbs provides 100% protection against this mixed SHIV challenge. These data reveal that single bNAbs efficiently select resistant viruses from a diverse challenge swarm to establish infection, demonstrating the importance of bNAb cocktails for HIV-1 prevention.