As blockchain technology evolves, it has become a crucial component in medical data sharing. However, current needs reveal that healthcare-focused blockchain schemes increasingly require the capabilities of modification and deletion. Moreover, traditional blockchain-based systems for medical data sharing often need help with a single point of failure, which undermines the system’s robustness. To address these challenges, we propose Redact-Chain for Health, a scheme based on the redactable blockchain for managing shared healthcare data. This scheme allows users to encrypt data for privacy protection and decrypt data when sharing medical information. By substituting the SHA-256 with the chameleon hash, Redact-Chain for Health introduces a fine-grained data editing scheme, facilitating medical institutions in effectively editing and managing data on the blockchain. Moreover, Redact-Chain for Health integrates a distributed trapdoor management scheme. This scheme empowers medical institutions to manage the trapdoor of the chameleon hash effectively, thereby circumventing the issue of a single point of failure. Our scheme also incorporates a symmetric encryption-based authentication algorithm to deter potential cyberattacks. Lastly, the security analysis of our proposed system demonstrates its effectiveness in preserving patients’ privacy, while performance analysis confirms Redact-Chain for Health’s efficiency.