Human immunodeficiency virus type 1 (HIV-1)-specific monoclonal antibodies with extraordinary potency and breadth have recently been described. In humanized mice, combinations of monoclonal antibodies have been shown to suppress viraemia, but the therapeutic potential of these monoclonal antibodies has not yet been evaluated in primates with an intact immune system. Here we show that administration of a cocktail of HIV-1-specific monoclonal antibodies, as well as the single glycan-dependent monoclonal antibody PGT121, resulted in a rapid and precipitous decline of plasma viraemia to undetectable levels in rhesus monkeys chronically infected with the pathogenic simian–human immunodeficiency virus SHIV-SF162P3. A single monoclonal antibody infusion afforded up to a 3.1 log decline of plasma viral RNA in 7 days and also reduced proviral DNA in peripheral blood, gastrointestinal mucosa and lymph nodes without the development of viral resistance. Moreover, after monoclonal antibody administration, host Gag-specific T-lymphocyte responses showed improved functionality. Virus rebounded in most animals after a median of 56 days when serum monoclonal antibody titres had declined to undetectable levels, although, notably, a subset of animals maintained long-term virological control in the absence of further monoclonal antibody infusions. These data demonstrate a profound therapeutic effect of potent neutralizing HIV-1-specific monoclonal antibodies in SHIV-infected rhesus monkeys as well as an impact on host immune responses. Our findings strongly encourage the investigation of monoclonal antibody therapy for HIV-1 in humans.