How to find proper moments to generate partial sentence translation given a streaming speech input? Existing approaches waiting-and-translating for a fixed duration often break the acoustic units in speech, since the boundaries between acoustic units in speech are not even. In this paper, we propose MoSST, a simple yet effective method for translating streaming speech content. Given a usually long speech sequence, we develop an efficient monotonic segmentation module inside an encoder-decoder model to accumulate acoustic information incrementally and detect proper speech unit boundaries for the input in speech translation task. Experiments on multiple translation directions of the MuST-C dataset show that outperforms existing methods and achieves the best trade-off between translation quality (BLEU) and latency. Our code is available at https://github.com/dqqcasia/mosst.