Background: Computationally derived quantitative imaging (radiomic) features that describe tumor phenotypes at the pixel level have demonstrated associations with clinical characteristics in early investigations of other cancers. This implies that molecular differences among tumors may be reflected in their structure on the scales probed by 3D magnetic resonance imaging (MRI). We investigated whether radiomic features computed over tumor volumes from pre-treatment breast MRI could predict risk factors in triple-negative breast cancer (TNBC). Methods: We evaluated breast tumors on pre-treatment, post-contrast T1-weighted MRI from 156 patients with non-metastatic TNBC who underwent neoadjuvant chemotherapy. Tumor regions of interest were segmented by a convolutional neural network algorithm, with validation by breast radiologists. Features quantifying tumor shape and texture were extracted for the largest tumor present in each patient. We identified 23 principal components (PCs) describing these data within the original 364-dimensional feature space for further analysis. Tumor volume was also extracted for comparison with the shape and texture PCs, clinical variables and outcomes, but was kept separate from other radiomic features, since it directly correlates with clinical stage. We compiled for the cohort clinical variables including demographics, stage, grade, and, where available, absolute lymphocyte count (ALC) and Ki-67, a cellular proliferation index routinely used in clinical practice. We then performed a series of univariate and multivariate regression analyses to identify radiomic PCs and clinical variables that significantly predict patient outcomes, and radiomic PCs that predict established risk factors. Our multivariate analyses utilized 5-fold cross-validation and Monte-Carlo determination of p-values (based on 3000 random samplings from the null hypothesis), to ensure statistical rigor in identifying predictive relationships while correcting for multiple hypothesis testing. Results: Our univariate analyses confirmed expected correlations between: overall survival and pre-treatment tumor volume (p = 0.010); survival and ALC (p = 0.002); and clinical stage and tumor volume (p = 1.2⨉10^-7). From our multivariate analysis, shape and texture radiomic features were predictive of: tumor volume (p < 0.001); clinical stage (p < 0.001); and Ki-67 (p = 0.02). We confirmed that Ki-67 was predictive of post-treatment residual cancer (p = 0.014), as has been previously reported. Conclusions: Radiomic features predict breast cancer risk factors that are significant for determining outcomes for TNBC patients. Combinations of radiomic shape and texture features track closely with tumor volumes, stage, and proliferative activity, potentially reflecting underlying molecular evolution.