Insurance agencies and digitally recorded healthcare databases can help society to decrease the high-level complexity and the cost of the entire healthcare ecosystem. The general data protection regulation provides the right to its data owner's to know how data is stored, and for which purpose his/her data is being used. However, the healthcare data flow through an open channel, i.e., the Internet, which opens the doors for intruders to perform some malicious activities, such as breach of confidential data, modification in the stored data, etc. So it is a challenging task for the traditional healthcare systems to maintain the security and privacy of the stakeholders. Blockchain is emerged as a technology that improves the efficiency of today's healthcare system and also helps to maintain the security and privacy of all the stakeholders. Motivated by these facts, in this paper, we analyse various security architectures used to secure electronic health records (EHRs) and apply Quantum Computing (QC) to the traditional encryption system. Then, we propose a blockchain-based architecture for Healthcare, which allows users to access the data from the database with their defined role. Further, to protect the traditional encryption system from the quantum attacks, the Quantum blind signature is used during the block creation using hyperledger Fabric blockchain. Results show the efficacy of the proposed scheme compared to the state-of-the-art schemes in terms of transaction throughput, resource consumption, and network traffic.