Human clinical studies investigating use of convalescent plasma (CP) for treatment of coronavirus disease 2019 (COVID-19) have produced conflicting results. Outcomes in these studies may vary at least partly due to different timing of CP administration relative to symptom onset. The mechanisms of action of CP include neutralizing antibodies but may extend beyond virus neutralization to include normalization of blood clotting and dampening of inflammation. Unresolved questions include the minimum therapeutic titer in the CP units or CP recipient as well as the optimal timing of administration. Here, we show that treatment of macaques with CP within 24 h of infection does not reduce viral shedding in nasal or lung secretions compared to controls and does not detectably improve any clinical endpoint. We also demonstrate that CP administration does not impact viral sequence diversity in vivo, although the selection of a viral sequence variant in both macaques receiving normal human plasma was suggestive of immune pressure. Our results suggest that CP, administered to medium titers, has limited efficacy, even when given very early after infection. Our findings also contribute information important for the continued development of the nonhuman primate model of COVID-19. These results should inform interpretation of clinical studies of CP in addition to providing insights useful for developing other passive immunotherapies and vaccine strategies. IMPORTANCE Antiviral treatment options for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) remain very limited. One treatment that was explored beginning early in the pandemic (and that is likely to be tested early in future pandemics) is plasma collected from people who have recovered from coronavirus disease 2019 (COVID-19), known as convalescent plasma (CP). We tested if CP reduces viral shedding or disease in a nonhuman primate model. Our results demonstrate that administration of CP 1 day after SARS-CoV-2 infection had no significant impact on viral loads, clinical disease, or sequence diversity, although treatment with normal human plasma resulted in selection of a specific viral variant. Our results demonstrate that passive immunization with CP, even during early infection, provided no significant benefit in a nonhuman primate model of SARS-CoV-2 infection.