The rebound-competent viral reservoir (RCVR), comprised of virus that is able to persist during antiretroviral therapy (ART) and mediate reactivation of systemic viral replication and rebound viremia after antiretroviral therapy interruption (ATI), remains the biggest obstacle to the eradication of HIV infection. A better understanding of the cellular and tissue origins and the dynamics of viral populations that initiate rebound upon ATI could help develop targeted therapeutic strategies for reducing the RCVR. In this study, barcoded SIVmac239M was used to infect rhesus macaques to enable monitoring of viral barcode clonotypes contributing to virus detectable in plasma after ATI. Blood, lymphoid tissues (LTs, spleen, mesenteric and inguinal lymph nodes), and non-lymphoid tissues (NLTs, colon, ileum, lung, liver, and brain) were analyzed using viral barcode sequencing, intact proviral DNA assay, single-cell RNA sequencing, and combined CODEX/RNAscope/in situ hybridization. Four of seven animals had viral barcodes detectable by deep sequencing of plasma at necropsy although plasma viral RNA remained < 22 copies/mL. Among the tissues studied, mesenteric and inguinal lymph nodes, and spleen contained viral barcodes detected in plasma, and trended to have higher cell-associated viral loads, higher intact provirus levels, and greater diversity of viral barcodes. CD4+ T cells were the main cell type harboring viral RNA (vRNA) after ATI. Further, T cell zones in LTs showed higher vRNA levels than B cell zones for most animals. These findings are consistent with LTs contributing to virus present in plasma early after ATI.