Electronic health record (EHR) management systems require the adoption of effective technologies when health information is being exchanged. Current management approaches often face risks that may expose medical record storage solutions to common security attack vectors. However, healthcare-oriented blockchain solutions can provide a decentralized, anonymous and secure EHR handling approach. This paper presents PREHEALTH, a privacy-preserving EHR management solution that uses distributed ledger technology and an Identity Mixer (Idemix). The paper describes a proof-of-concept implementation that uses the Hyperledger Fabric's permissioned blockchain framework. The proposed solution is able to store patient records effectively whilst providing anonymity and unlinkability. Experimental performance evaluation results demonstrate the scheme's efficiency and feasibility for real-world scale deployment.