With magnetic resonance imaging (MRI), the segmentation of breast lesions is helpful for early diagnosis. Since it is subjective and time-consuming for physicians to delineate the lesions, automatic segmentation is in active demand. However, the low contrast and small size of the lesions will cause difficulties in existing segmentation methods. In this paper, we propose a three-stream interactive neural network (TSINet) for the efficient segmentation of MRI breast lesions. TSINet uses three streams for extracting boundary information, location information and predicting lesion masks, respectively. The boundary extraction stream enhances the representation of boundary pixels based on gate convolution. The internal location stream that works based on the attention mechanism identifies the location of the lesions. The lesion segmentation stream fuse the boundary and location information to accurately segment the lesion. We collect MRI data from 248 breast patients at the Second Hospital of Dalian Medical University to evaluate TSINet. The results demonstrate that the TSINet can delineate lesion boundaries close to that drawn by physicians, and outperform state-of-the-art methods.