Recently, an infectious disease, coronavirus disease 2019 (COVID-19), has been reported in Wuhan, China, and spread worldwide within a couple of months. There have been seen an outbreak of COVID-19 in many countries, where the infected patients' rate overwhelmed the inadequate medical services. The push of patient-centered interoperability (PCI) from medical institution-centered interoperability may defeat the current and post resultant disease of the COVID-19 pandemic. This paper proposes a state-of-the-art privacy-preserving medical data sharing system based on Hyperledger Fabric (MedHypChain), where each transaction is secured via an Identity-based broadcast group signcryption scheme. We proved that MedHypChain achieves confidentiality, anonymity, traceability, and unforgeability. Besides, we regularize the MedHypChain to implement the PCI healthcare system, where the patient manages its health-related information in the blockchain that can be accessible to the authorized entity. We also use the Hyperledger caliber as a benchmark tool to analyze the performance of MedHypChain in three metrics (latency time, execution time, and throughput) for up to 20 permissioned nodes. Finally, we compare MedHypChain with related blockchain-based healthcare systems and found that the proposed scheme needs the least computation cost and communication cost and achieves all security features, such as authenticity, scalability, and access control.