Rotator cuff tear (RCT) is one of the most common shoulder injuries, which can be irreparable if it develops to a severe condition. A portable imaging system for the on-site detection of RCT is necessary to identify its extent for early diagnosis. We introduce a microwave tomography system, using state-of-the-art numerical modeling and parallel computing for detection of RCT. The results show that the proposed method is capable of accurately detecting and localizing this injury in different size. In the next step, an efficient design in terms of computing time and complexity is proposed to detect the variations in the injured model with respect to the healthy model. The method is based on finite element discretization and uses parallel preconditioners from the domain decomposition method to accelerate computations. It is implemented using the open source FreeFEM software.