Health care is undergoing a big data revolution, with vast amounts of information supplied from numerous sources, leading to major paradigm shifts including precision medicine and AI driven healthcare among others. Yet, there still exist significant barriers before such approaches could be adopted in practice, including data integration and interoperability, data sharing, security and privacy protection, scalability, and policy and regulatory issues. Blockchain provides a unique opportunity to tackle major challenges in health care and biomedical research, such as enabling data sharing and integration for patient-centered care, data provenance allowing verification authenticity of the data, and optimization of some of the health care processes among others. Nevertheless, technological constraints of current blockchain technologies necessitate further research before mass adoption of blockchain-based healthcare data management is possible. We analyze context-based requirements and capabilities of the available technology and propose a research agenda and new approaches towards achieving intelligent healthcare data management using blockchain.