Efforts to identify driver mutations in cancer have largely focused on genes, whereas non-coding sequences remain relatively unexplored. Here we develop a statistical method based on characteristics known to influence local mutation rate and a series of enrichment filters in order to identify distal regulatory elements harboring putative driver mutations in breast cancer. We identify ten DNase I hypersensitive sites that are significantly mutated in breast cancers and associated with the aberrant expression of neighboring genes. A pan-cancer analysis shows that three of these elements are significantly mutated across multiple cancer types and have mutation densities similar to protein-coding driver genes. Functional characterization of the most highly mutated DNase I hypersensitive sites in breast cancer (using in silico and experimental approaches) confirms that they are regulatory elements and affect the expression of cancer genes. Our study suggests that mutations of regulatory elements in tumors likely play an important role in cancer development.