Persistent and uncontrolled SARS-CoV-2 replication in immunocompromised individuals has been observed and may be a contributing source of novel viral variants that continue to drive the pandemic. Importantly, the effects of immunodeficiency associated with chronic HIV infection on COVID-19 disease and viral persistence have not been directly addressed in a controlled setting. Here we conducted a pilot study wherein two pigtail macaques (PTM) chronically infected with SIVmac239 were exposed to SARS-CoV-2 and monitored for six weeks for clinical disease, viral replication, and viral evolution, and compared to our previously published cohort of SIV-naïve PTM infected with SARS-CoV-2. At the time of SARS-CoV-2 infection, one PTM had minimal to no detectable CD4+ T cells in gut, blood, or bronchoalveolar lavage (BAL), while the other PTM harbored a small population of CD4+ T cells in all compartments. Clinical signs were not observed in either PTM; however, the more immunocompromised PTM exhibited a progressive increase in pulmonary infiltrating monocytes throughout SARS-CoV-2 infection. Single-cell RNA sequencing (scRNAseq) of the infiltrating monocytes revealed a less activated/inert phenotype. Neither SIV-infected PTM mounted detectable anti-SARS-CoV-2 T cell responses in blood or BAL, nor anti-SARS-CoV-2 neutralizing antibodies. Interestingly, despite the diminished cellular and humoral immune responses, SARS-CoV-2 viral kinetics and evolution were indistinguishable from SIV-naïve PTM in all sampled mucosal sites (nasal, oral, and rectal), with clearance of virus by 3-4 weeks post infection. SIV-induced immunodeficiency significantly impacted immune responses to SARS-CoV-2 but did not alter disease progression, viral kinetics or evolution in the PTM model. SIV-induced immunodeficiency alone may not be sufficient to drive the emergence of novel viral variants.