The Hyperledger Fabric (HF) framework is widely studied for securing electronic health records (EHRs) in the healthcare sector. Despite the various cross-domain blockchain technology (BCT) applications, little is known about the role of the HF framework in healthcare. The purpose of the systematic literature review (SLR) is to review the existing literature on the HF framework and its applications in healthcare. This SLR includes literature published between January 2015 and March 2023 in the ACM digital library, IEEE Xplore, SCOPUS, Springer, PubMed, and Google Scholar databases. Following the inclusion and exclusion criteria, a total of 57 articles emerged as eligible for this SLR. The HF framework was found to be useful in securing health records coming from the Internet of Medical Things (IoMT) and many other devices. The main causes behind using the HF framework were identified as privacy and security, integrity, traceability, and availability of health records. Additionally, storage issues with transactional data over the blockchain are reduced by the use of the HF framework. This SLR also highlights potential future research trends to ensure the high-level security of health records.