MoE-Health is a novel Mixture of Experts framework for healthcare prediction. It utilizes medical data from various modalities, including electronic health records (EHRs), clinical notes, and medical images, to perform clinical predictions. Unlike existing methods that require complete modality data or rely on manual selection strategies, MoE-Health is designed to handle real-world samples with diverse or incomplete modality data. It flexibly adapts to diverse data availability scenarios by dynamically selecting and combining relevant experts based on available data modalities, leveraging a specialized expert network and a dynamic gating mechanism. It was evaluated on the MIMIC-IV dataset for three clinical prediction tasks: in-hospital mortality prediction, long-term hospitalization prediction, and readmission prediction, and achieved superior performance compared to existing multi-modality fusion methods.