Breast cancer is the second most common cancer type and is the leading cause of cancer-related deaths worldwide. Since it is a heterogeneous disease, subtyping breast cancer plays an important role in performing a specific treatment. Gene expression data is a viable alternative to be employed on cancer subtype classification, as they represent the state of a cell at the molecular level, but generally has a relatively small number of samples compared to a large number of genes. Gene selection is a promising approach that addresses this uneven high-dimensional matrix of genes versus samples and plays an important role in the development of efficient cancer subtype classification. In this work, an innovative outlier-based gene selection (OGS) method is proposed to select relevant genes for efficiently and effectively classify breast cancer subtypes. Experiments show that our strategy presents an $F_{1}$ score of 1.0 for basal and 0.86 for her 2, the two subtypes with the worst prognoses, respectively. Compared to other methods, our proposed method outperforms in the $F_{1}$ score using 80% less genes. In general, our method selects only a few highly relevant genes, speeding up the classification, and significantly improving the classifier’s performance.