Cuproptosis is a novel form of copper‐induced programmed cell death. Here, we investigate the role of cuproptosis‐related genes in head and neck squamous cell carcinoma (HNSCC), and the correlations between cuproptosis‐related genes and tumor‐infiltrating immune cells in the microenvironment. Gene expression data were downloaded from TCGA and analyzed using R. Protein–protein interaction analysis was conducted using STRING and GeneMANIA, while survival analyses examined the correlations between genes and overall survival. In addition, analyses of methylation and mutation sites were performed using Illumina HumanMethylation450 data and the cBioPortal data set, respectively. The correlations between gene expression level and infiltrating immune cells and predictive values of PD‐1/PD‐L1 blockade responses were also analyzed. Cuproptosis‐promoting genes were downregulated, while two out of three cuproptosis‐inhibiting genes, GLS and CDKN2A, showed upregulated expression. The CDKN2A expression level was identified as an independent prognostic factor for HNSCC through the multivariate Cox survival analysis. Meanwhile, levels of all cuproptosis‐related genes correlated positively with CD4+ T cell infiltration. Furthermore, expression of the cuproptosis‐promoting gene DLD was negatively correlated with immune score. All cuproptosis‐related genes were expressed aberrantly and correlated positively with CD4+ T cell infiltration in HNSCC. Thus, copper homeostasis and cuproptosis could be targeted therapeutically as a potential means of enhancing the efficacy of immunotherapy.