Vaccination of the global population against COVID-19 is one of the challenging tasks in supply chain management that humanity has ever faced. The rapid roll-out of the COVID-19 vaccine is a must for making the worldwide immunization campaign successful, but its effectiveness depends on the availability of an operational and transparent distribution chain that can be audited by all related stakeholders. In this paper, the necessity of Blockchain and Machine Learning in supply-chain management with demand forecasting of the COVID-19 vaccine has been presented. The aim is to understand how the convergence of Blockchain technology and ML monitor the prerequisite of vaccine distribution with demand forecasting. Here, we have proposed an approach consists of Blockchain and Machine Learning which will be used to ensure the seamless COVID-19 vaccine distribution with transparency, data integrity, and end-to-end traceability for reducing risk, assuring the safety, and also immutability. Besides this, we have performed demand forecasting for appropriate COVID-19 vaccines according to the geographical area and the storage facilities. Lastly, we have discussed research challenges and also mentioning the limitations with future directions.