Recent technological advancements have led to the development of new methods for managing organ donation systems, which aim to overcome the limitations of traditional centralized systems. To achieve increased transparency, security, and efficiency in the organ donation process, blockchain technology is being proposed as a replacement for these centralized systems. However, most previous works on organ donation systems have focused on using Ethereum-based blockchain solutions, which offer limited control, a fixed set of consensus protocols, and no support for concurrent executions. In contrast, our work has utilized the Hyperledger Fabric framework to develop a network model of the organ donation system. We have designed and deployed a prototype system with smart contracts using Amazon Managed Blockchain Service. Additionally, we have built a client application that uses the Fabric SDK to interact with the network and perform various actions. To evaluate the performance of our system, we conducted extensive testing using the Hyperledger Caliper benchmarking tool. In our test bench, the system achieved a peak actual send rate of 389.1 transactions per second (TPS) for creating new records and 508.4 TPS for reading records. At a send rate of 800 TPS, the system took an average of 12.16 seconds to serve a request for creating a record and an average of 3.71 seconds to serve a request for reading a record. Future work is required to extend the functionalities of the system and identify potential endorsers and managers for this type of controlled blockchain network.