Breast tumor segmentation based on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) remains an active as well as a challenging problem. Previous studies often rely on manual annotation for tumor regions, which is not only time-consuming but also error-prone. Recent studies have shown high promise of deep learning-based methods in various segmentation problems. However, these methods are usually faced with the challenge of limited number (e.g., tens or hundreds) of medical images for training, leading to sub-optimal segmentation performance. Also, previous methods cannot efficiently deal with prevalent class-imbalance problems in tumor segmentation, where the number of voxels in tumor regions is much lower than that in the background area. To address these issues, in this study, we propose a mask-guided hierarchical learning (MHL) framework for breast tumor segmentation via fully convolutional networks (FCN). Our strategy is first decomposing the original difficult problem into several sub-problems and then solving these relatively simpler sub-problems in a hierarchical manner. To precisely identify locations of tumors that underwent a biopsy, we further propose an FCN model to detect two landmarks defined on nipples. Finally, based on both segmentation probability maps and our identified landmarks, we proposed to select biopsied tumors from all detected tumors via a tumor selection strategy using the pathology location. We validate our MHL method using data for 272 patients, and achieve a mean Dice similarity coefficient (DSC) of 0.72 in breast tumor segmentation. Finally, in a radiogenomic analysis, we show that a previously developed image features show a comparable performance for identifying luminal A subtype when applied to the automatic segmentation and a semi-manual segmentation demonstrating a high promise for fully automated radiogenomic analysis in breast cancer.