Stroke disrupts brain function beyond focal lesions, altering multiscale temporal dynamics essential for information processing. We investigated intrinsic neural timescales (INT) and other properties of long-range temporal correlations, using longitudinal fMRI data from 15 ischemic stroke patients across 6 months, and compared them to age-matched controls. Results show that stroke patients exhibited significantly prolonged INT in multiple cortical regions, reflecting slowed temporal dynamics and disrupted hierarchy. These dynamic changes persisted through recovery and were more pronounced in patients with poor outcomes, especially within cognitive control networks. Computational modeling suggested that stroke-induced INT prolongation driven by heightened neuronal excitability reflects a dynamic shift towards criticality. Our findings position long-range temporal correlations and INT as potential biomarkers for monitoring and predicting functional recovery. This framework provides a novel perspective on stroke-induced brain changes and suggests avenues for targeted neurorehabilitation using interventions aiming at restoring intrinsic temporal dynamics.