Sensitive information is a classified type of content that should not be disclosed to the public. And that would harm the owner of the information if it is disclosed. The collaboration between organizations, institutions, and individuals leads to a huge amount of information generation and sharing. Sharing of such information will come with disclose of sensitive information. Sensitive information can be organizational, governmental, or personal. However, whatever its type is, it needs proper handling and protection. To protect disclose of sensitive information, first it requires detecting the availability of sensitive information and its domain classification for further analysis. To the best of our knowledge, there is no work attempted for Amharic texts. Models developed for another language cannot be used for Amharic texts language because of morphology, grammar, and semantics differences. To address these gaps, we have developed a model for detecting and classifying sensitive personal information for Amharic texts. We proposed Bi-LSTM based model for sensitive information detection and classification. We have experimented with the three deep learning algorithms: LSTM, BI-LSTM, and CNN using 7.31K and 6.697K Amharic sentences for sensitivity detection and domain classification respectively on three experiments. The accuracy of LSTM, BI-LSTM, and CNN was 84%, 91%, and 88% for sensitivity classification and 88%, 93%, and 89% for domain classification respectively. The proposed Bi-LSTM model outperforms Both CNN and LSTM.