Privacy concerns in healthcare data management necessitate secure and private handling of highly sensitive information. This paper investigates the application of Hyperledger Fabric (HLF) to enhance privacy and security in healthcare, with a focus on medication adherence as a critical use case. We examine HLF's privacy-preserving mechanisms, including the Certificate Authority, channels, and Private Data Collections. These mechanisms facilitate secure data sharing among doctors, pharmacists, and patients without compromising data privacy and integrity. Our research presents a proof-of- concept implementation demonstrating how HLF can ensure secure storage, data integrity, privacy, patient data ownership, and traceability throughout the medication adherence process. By implementing a decentralized approach, we highlight HLF's capability to provide a scalable solution for managing sensitive healthcare data, thus contributing to improved medication adherence outcomes. This work not only showcases the practical applicability of blockchain in healthcare but also opens avenues for future research on privacy-preserving technologies in this domain.