Automatic segmentation of shoulder muscle MRI is challenging due to the high variation in muscle size, shape, texture, and spatial position of tears. Manual segmentation of tear and muscle portion is hard, time-consuming, and subjective to pathological expertise. This work proposes a new Region and Edge-based Deep Auto-Encoder (RE-DAE) for shoulder muscle MRI segmentation. The proposed RE-DAE harmoniously employs average and max-pooling operation in the encoder and decoder blocks of the Convolutional Neural Network (CNN). Region-based segmentation incorporated in the Deep Auto-Encoder (DAE) encourages the network to extract smooth and homogenous regions. In contrast, edge-based segmentation tries to learn the boundary and anatomical information. These two concepts, systematically combined in a DAE, generate a discriminative and sparse hybrid feature space (exploiting both region homogeneity and boundaries). Moreover, the concept of static attention is exploited in the proposed RE-DAE that helps in effectively learning the tear region. The performances of the proposed MRI segmentation based DAE architectures have been tested using a 3D MRI shoulder muscle dataset using the hold-out cross-validation technique. The MRI data has been collected from the Korea University Anam Hospital, Seoul, South Korea. Experimental comparisons have been conducted by employing innovative custom-made and existing pre-trained CNN architectures both using transfer learning and fine-tuning. Objective evaluation on the muscle datasets using the proposed SA-RE-DAE showed a dice similarity of 85.58% and 87.07%, an accuracy of 81.57% and 95.58% for tear and muscle regions, respectively. The high visual quality and the objective result suggest that the proposed SA-RE-DAE is able to correctly segment tear and muscle regions in shoulder muscle MRI for better clinical decisions.