Recent studies showed preliminary data on associations of MRI-based imaging phenotypes of breast tumours with breast cancer molecular, genomic, and related characteristics. In this study, we present a comprehensive analysis of this relationship. We analysed a set of 922 patients with invasive breast cancer and pre-operative MRI. The MRIs were analysed by a computer algorithm to extract 529 features of the tumour and the surrounding tissue. Machine-learning-based models based on the imaging features were trained using a portion of the data (461 patients) to predict the following molecular, genomic, and proliferation characteristics: tumour surrogate molecular subtype, oestrogen receptor, progesterone receptor and human epidermal growth factor status, as well as a tumour proliferation marker (Ki-67). Trained models were evaluated on the set of the remaining 461 patients. Multivariate models were predictive of Luminal A subtype with AUC = 0.697 (95% CI: 0.647–0.746, p < .0001), triple negative breast cancer with AUC = 0.654 (95% CI: 0.589–0.727, p < .0001), ER status with AUC = 0.649 (95% CI: 0.591–0.705, p < .001), and PR status with AUC = 0.622 (95% CI: 0.569–0.674, p < .0001). Associations between individual features and subtypes we also found. There is a moderate association between tumour molecular biomarkers and algorithmically assessed imaging features.