Human leukocyte antigen class I (HLA-I) molecules present intracellular peptides on the cell surface to enable CD8+ T cells to effectively control viral infections. Many viruses disrupt this antigen presentation pathway to evade immune detection. In this study, we demonstrate that SARS-CoV-2 Nsp1 impairs both the constitutive and interferon-γ (IFN-γ)-induced upregulation of HLA-I. Moreover, Nsp1 also blocks IFN-γ-induced expression of HLA-II. We found that, contrary to previously published work, the early SARS-CoV-2 B 1.1.7 Alpha variant lacking the accessory protein ORF8 retained full capacity to downregulate HLA-I, comparable to an ORF8-expressing wild-type isolate. While ectopic overexpression of ORF8 could reduce HLA-I surface levels, this effect was only observed at high expression levels. In contrast, moderate expression of the viral protein Nsp1 was sufficient to potently suppress both basal and IFN-γ-induced HLA-I, as well as HLA-II expression. To probe the underlying mechanism, we analyzed HLA-I-associated genes in previously published RNA-sequencing datasets and confirmed that Nsp1 reduces expression of components required for HLA-I biosynthesis and antigen processing. These findings identify Nsp1 as a key factor that impairs antigen presentation pathways, potentially contributing to the ability of SARS-CoV-2 to modulate immune recognition.