The early detection of neurodegenerative disorders such as Alzheimer’s disease is crucial to providing effective healthcare for management and recovery. We address the task of ternary classification of healthy, mild cognitive impairment, and Alzheimer’s disease categories from multiple data modalities of 3D MRIs, patient electronic health records, and genetic information. For this task, we propose a Dynamic Attention Guided Multi-modal Fusion (DAGMF) approach, broadly consisting of three deep network components. The first component independently performs feature extraction for all modalities and refines them using novel Per-Modality Attention blocks. Thereafter, the obtained modality representations are provided to a proposed Dynamic Attention Multi-modal Solver block, which models the dynamics of attention across learning iterations by a Neural Ordinary Differential Equation (NODE) solver to generate modality attention. The modality representations and attention are finally provided to a novel Attention-induced Multi-modal Fusion block, which uses the attention to perform late-fusion of the multiple modality representations by a second NODE solver, which models dynamics of the various modalities across learning iterations. Empirical studies on multi-modal datasets constructed from the ADNI collection show that the proposed DAGMF method provides better classification performance than state-of-the-art multi-modal deep learning approaches.