The application of next‐generation sequencing (NGS) to non‐invasive samples is one of the most promising methods in conservation genomics, but these types of samples present significant challenges for NGS. The European mink (Mustela lutreola) is critically endangered throughout its range. However, important aspects such as census size and inbreeding remain still unknown in many populations, so it is crucial to develop new methods to monitor this species. In this work, we placed hair tubes along riverbanks in a border area of the Iberian population, which allowed the genetic identification of 76 European mink hair samples. We then applied a reduced representation genomic sequencing (ddRAD) technique to a subset of these samples to test whether we could extract sufficient genomic information from them. We show that several problems with the DNA, including contamination, fragmentation, oxidation, and possibly sample mixing, affected the samples. Using various bioinformatic techniques to reduce these problems, we were able to unambiguously genotype 19 hair samples belonging to six individuals. This small number of individuals showed that the demographic status of the species in this peripheral population is worse than expected. The data obtained also allowed us to perform preliminary analyses of relatedness and inbreeding. Although further improvements in sampling and analysis are needed, the application of the ddRAD technique to non‐invasively obtained hairs represents a significant advance in the genomic study of endangered species.