Melanoma is the most lethal type of skin cancer with an increasing incidence. Cuproptosis is the most recently identified copper-dependent form of cell death that relies on mitochondrial respiration. The hippocampal (Hippo) pathway functions as a tumor suppressor by regulating Yes-associated protein/transcriptional coactivator with PDZ-binding motif (YAP/TAZ) activity. However, its role in cuproptosis remains unknown. In addition, the correlation of cuproptosis-related genes and Hippo pathway-related genes with tumor prognosis warrants further investigation. In the present study, we explored the correlation of cuproptosis-related genes and Hippo pathway-related genes with the prognosis of melanoma through analysis of data from a public database and experimental verification. We found eight Hippo pathway-related genes that were downregulated in melanoma and exhibited predictive value for prognosis. There was a significant positive correlation between cuproptosis-related genes and Hippo pathway-related genes in skin cutaneous melanoma. YAP1 expression was positively correlated with ferredoxin 1 (FDX1) expression in the GSE68599 dataset and A2058 cells. Moreover, YAP1 was positively and negatively correlated with M2 macrophages and regulatory T cell infiltration, respectively. In conclusion, the present study demonstrated the prognostic value of Hippo pathway-related genes (particularly YAP1) in melanoma, revealing the correlation between the expression of Hippo pathway-related genes and immune infiltration. Thus, the present findings may provide new clues on the prognostic assessment of patients with melanoma and a new target for the immunotherapy of this disease.