Immunization brings about significant health, economic, and social benefits worldwide. However, vaccine supply networks encounter persistent challenges, including unpredictable demand forecasting, the circulation of counterfeit vaccines, and inadequate coordination among stakeholders. These issues hinder access to vaccines and impede the achievement of public health objectives. The COVID-19 pandemic has further disrupted vaccine supply chains, intensifying existing vulnerabilities. To address these challenges, this study proposes an intelligent vaccine supply management system that integrates blockchain technology, Internet of Things (IoT) sensors, and machine learning algorithms. The blockchain architecture fosters transparency and credibility by recording tamper-proof transactions across the entire vaccine production and delivery process. IoT sensors inserted in vaccine vials enable real-time tracking and temperature monitoring to ensure quality preservation. Moreover, transformer-based neural networks analyze supply chain data on the blockchain to precisely predict vaccine demand within 5% of actual needs, facilitating data-driven production planning. This innovative combination of blockchain traceability, IoT monitoring, and machine learning analytics enhances vaccine supply chain visibility, coordination, and performance. Simulation results indicate over 90% accuracy in projecting vaccine requirements based on historical data patterns. The proposed system offers a robust digital solution to overcome vaccine supply deficiencies resulting from endemic and pandemic-induced challenges by promoting supply chain transparency, accountability, and intelligence.