In untreated HIV-1 infection, rapid viral evolution allows escape from immune responses. Viral replication can be blocked by antiretroviral therapy. However, HIV-1 persists in a latent reservoir in resting CD4⁺ T cells, and rebound viremia occurs following treatment interruption. The reservoir, which is maintained in part by clonal expansion, can be measured using quantitative viral outgrowth assays (QVOAs) in which latency is reversed with T cell activation to allow viral outgrowth. Recent studies have shown that viruses detected in QVOAs prior to treatment interruption often differ from rebound viruses. We hypothesized that autologous neutralizing antibodies directed at the HIV-1 envelope (Env) protein might block outgrowth of some reservoir viruses. We modified the QVOA to reflect pressure from low concentrations of autologous antibodies and showed that outgrowth of a substantial but variable fraction of reservoir viruses is blocked by autologous contemporaneous immunoglobulin G (IgG). A reduction in outgrowth of >80% was seen in 6 of 15 individuals. This effect was due to direct neutralization. We established a phylogenetic relationship between rebound viruses and viruses growing out in vitro in the presence of autologous antibodies. Some large infected cell clones detected by QVOA carried neutralization-sensitive viruses, providing a cogent explanation for differences between rebound virus and viruses detected in standard QVOAs. Measurement of the frequency of reservoir viruses capable of outgrowth in the presence of autologous IgG might allow more accurate prediction of time to viral rebound. Ultimately, therapeutic immunization targeting the subset of variants resistant to autologous IgG might contribute to a functional cure.