Anemia is a prevalent hematological disorder that requires frequent hemoglobin monitoring for early diagnosis and effective management. Conventional hemoglobin assessment relies on invasive blood sampling, limiting its suitability for large-scale or continuous screening. This paper presents a non-invasive framework for hemoglobin estimation and anemia screening using multichannel photoplethysmography (PPG) signals and explainable artificial intelligence. Four-wavelength PPG signals (660, 730, 850, and 940~nm) are processed to extract optical and cross-wavelength features, which are aggregated at the subject level to avoid data leakage. A gradient boosting regression model is employed to estimate hemoglobin concentration, followed by post-regression anemia screening using World Health Organization (WHO) thresholds. Model interpretability is achieved using SHapley Additive explanations (SHAP), enabling both global and subject-specific analysis of feature contributions. Experimental evaluation on a publicly available dataset demonstrates a mean absolute error of 8.50 plus minus 1.27 and a root mean squared error of 8.21~g/L on unseen test subjects, indicating the potential of the proposed approach for interpretable, non-invasive hemoglobin monitoring and preliminary anemia screening.