Using quantitative radiomics, we demonstrate that computer-extracted magnetic resonance (MR) image-based tumor phenotypes can be predictive of the molecular classification of invasive breast cancers. Radiomics analysis was performed on 91 MRIs of biopsy-proven invasive breast cancers from National Cancer Institute's multi-institutional TCGA/TCIA. Immunohistochemistry molecular classification was performed including estrogen receptor, progesterone receptor, human epidermal growth factor receptor 2, and for 84 cases, the molecular subtype (normal-like, luminal A, luminal B, HER2-enriched, and basal-like). Computerized quantitative image analysis included: three-dimensional lesion segmentation, phenotype extraction, and leave-one-case-out cross validation involving stepwise feature selection and linear discriminant analysis. The performance of the classifier model for molecular subtyping was evaluated using receiver operating characteristic analysis. The computer-extracted tumor phenotypes were able to distinguish between molecular prognostic indicators; area under the ROC curve values of 0.89, 0.69, 0.65, and 0.67 in the tasks of distinguishing between ER+ versus ER-, PR+ versus PR-, HER2+ versus HER2-, and triple-negative versus others, respectively. Statistically significant associations between tumor phenotypes and receptor status were observed. More aggressive cancers are likely to be larger in size with more heterogeneity in their contrast enhancement. Even after controlling for tumor size, a statistically significant trend was observed within each size group (P = 0.04 for lesions ≤ 2 cm; P = 0.02 for lesions >2 to ≤5 cm) as with the entire data set (P-value = 0.006) for the relationship between enhancement texture (entropy) and molecular subtypes (normal-like, luminal A, luminal B, HER2-enriched, basal-like). In conclusion, computer-extracted image phenotypes show promise for high-throughput discrimination of breast cancer subtypes and may yield a quantitative predictive signature for advancing precision medicine.