Persistence of the rebound-competent viral reservoir (RCVR) within the CD4+ T cell compartment of people living with HIV remains a major barrier to HIV cure. Here, we determined the effects of the pan-lymphocyte-depleting monoclonal antibody (mAb) alemtuzumab on the RCVR in SIVmac239-infected rhesus macaques (RM) receiving antiretroviral therapy (ART). Alemtuzumab administered during chronic ART or at the time of ART initiation induced >95% depletion of circulating CD4+ T cells in peripheral blood and substantial CD4+ T cell depletion in lymph nodes. However, treatment was followed by proliferation and reconstitution of CD4+ T cells in blood, and despite ongoing ART, levels of cell-associated SIV DNA in blood and lymphoid tissues were not substantially different between alemtuzumab-treated and control RM after immune cell reconstitution, irrespective of the time of alemtuzumab treatment. Upon ART cessation, 19 of 22 alemtuzumab-treated RM and 13 of 13 controls rebounded with no difference in the time to rebound between treatment groups. Time to rebound and reactivation rate was associated with plasma viral loads (pVLs) at time of ART initiation, suggesting lymphocyte depletion had no durable impact on the RCVR. However, 3 alemtuzumab-treated RM that had lowest levels of pre-ART viremia, failed to rebound after ART withdrawal, in contrast to controls with similar levels of SIV replication. These observations suggest that alemtuzumab therapy has little to no ability to reduce well-established RCVRs but may facilitate RCVR destabilization when pre-ART virus levels are particularly low.