To develop targeted treatments, it is crucial to identify the full spectrum of genetic drivers in melanoma, including those in non-coding regions. However, recent efforts to explore non-coding regions have primarily focused on gene-adjacent elements such as promoters and non-coding RNAs, leaving intergenic distal regulatory elements largely unexplored. We used Hi-C chromatin contact data from melanoma cells to map distal, non-coding, promoter-interacting regulatory elements genome-wide in melanoma. Using this "promoter-interaction network", alongside whole-genome sequence and gene expression data from the Pan Cancer Analysis of Whole Genomes, we developed multivariate linear regression models to identify distal somatic mutation hotspots that affect promoter activity. We identified eight recurrently mutated hotspots that are novel, melanoma-specific, located in promoter-interacting distal regulatory elements, alter transcription factor binding motifs, and affect the expression of genes (e.g., HSPB7, CLDN1, ADCY9 and FDXR) previously implicated as tumour suppressors/oncogenes in various cancers. Our study suggests additional non-coding drivers beyond the well-characterised TERT promoter in melanoma, offering new insights into the disruption of complex regulatory networks by non-coding mutations that may contribute to melanoma development. Furthermore, our study provides a framework for integrating multiple levels of biological data to uncover cancer-specific non-coding drivers.