Post-stroke cognitive impairment (PSCI) is a common and debilitating consequence of stroke that often arises from complex interactions between diverse brain alterations. The accurate early prediction of PSCI is critical for guiding personalized interventions. However, existing methods often struggle to capture complex structural disruptions and integrate multimodal information effectively. This study proposes the multimodal dynamic hierarchical clustering network (MDHCNet), a graph neural network designed for accurate and interpretable PSCI prediction. MDHCNet constructs brain graphs from diffusion-weighted imaging, magnetic resonance angiography, and T1- and T2-weighted images and integrates them with clinical features using a hierarchical cross-modal fusion module. Experimental results using a real-world stroke cohort demonstrated that MDHCNet consistently outperformed deep learning baselines. Ablation studies validated the benefits of multimodal fusion, while saliency-based interpretation highlighted discriminative brain regions associated with cognitive decline. These findings suggest that MDHCNet is an effective and explainable tool for early PSCI prediction, with the potential to support individualized clinical decision-making in stroke rehabilitation.