Small and medium enterprises (SMEs) play a crucial role in supporting the global economy by contributing significantly to employment and value creation. Therefore, accurately predicting early signs of financial distress in SMEs and taking timely management improvement actions is of paramount importance. However, there is a lack of research on developing multi-class financial distress prediction (MFDP) models specifically for SMEs. Moreover, traditional MFDP models often lack interpretability. To address this, this study proposes definitions for multi-class financial distress in SMEs and constructs a MFDP model using machine learning. Additionally, it introduces an explainable framework to interpret the constructed model. Specifically, the study classifies SMEs' financial conditions into three categories: healthy, mild financial distress, and severe financial distress. It conducts a comparative analysis of six machine learning models. Furthermore, it proposes new interpretation methods for the MFDP model using SHapley Additive exPlanations (SHAP) and counterfactual explanations (CE), both of which are explainable artificial intelligence techniques. The empirical results reveal that the MFDP model, which adjusts data balance using random oversampling and integrates LightGBM with a one-versus-rest decomposition method, demonstrates the highest performance. Moreover, the proposed explainable framework demonstrates that it can provide practical and concrete improvement strategies to the model users, such as managers and financial institutions.