Hebrew manuscripts preserve thousands of textual transmissions of post-Biblical Hebrew texts from the first millennium. In many cases, the text in the manuscripts is not fully decipherable, whether due to deterioration, perforation, burns, or otherwise. Existing BERT models for Hebrew struggle to fill these gaps, due to the many orthographical deviations found in Hebrew manuscripts. We have pretrained a new dedicated BERT model, dubbed MsBERT (short for: Manuscript BERT), designed from the ground up to handle Hebrew manuscript text. MsBERT substantially outperforms all existing Hebrew BERT models regarding the prediction of missing words in fragmentary Hebrew manuscript transcriptions in multiple genres, as well as regarding the task of differentiating between quoted passages and exegetical elaborations. We provide MsBERT for free download and unrestricted use, and we also provide an interactive and user-friendly website to allow manuscripts scholars to leverage the power of MsBERT in their scholarly work of reconstructing fragmentary Hebrew manuscripts.