Breast cancer is a heterogeneous disease and one of the most common cancers among women. Recently, microRNAs (miRNAs) have been used as biomarkers due to their effective role in cancer diagnosis. This study proposes a support vector machine (SVM)-based classifier SVM-BRC to categorize patients with breast cancer into early and advanced stages. SVM-BRC uses an optimal feature selection method, inheritable bi-objective combinatorial genetic algorithm, to identify a miRNA signature which is a small set of informative miRNAs while maximizing prediction accuracy. MiRNA expression profiles of a 386-patient cohort of breast cancer were retrieved from The Cancer Genome Atlas. SVM-BRC identified 34 of 503 miRNAs as a signature and achieved a 10-fold cross-validation mean accuracy, sensitivity, specificity, and Matthews correlation coefficient of 80.38%, 0.79, 0.81, and 0.60, respectively. Functional enrichment of the 10 highest ranked miRNAs was analysed in terms of Kyoto Encyclopedia of Genes and Genomes and Gene Ontology annotations. Kaplan-Meier survival analysis of the highest ranked miRNAs revealed that four miRNAs, hsa-miR-503, hsa-miR-1307, hsa-miR-212 and hsa-miR-592, were significantly associated with the prognosis of patients with breast cancer.