This study attempts to explain the development and progress of the technology used for sharing health information across health care organizations (such as hospitals and physicians' offices). First, we describe the strengths and weaknesses of traditional sharing models, health information exchange (HIE), and blockchain-based HIE. Second, the potential use of nonfungible token (NFT) protocols in HIE models is proposed as the next possible move for information-sharing initiatives in health care. In addition to some potential opportunities and distinguishing features (eg, ownability, verifiability, and incentivization), we identify the uncertainty and risks associated with the application of NFTs, such as the lack of a dedicated regulatory framework for legal ownership of digital patient data. This paper is among the first to discuss the potential of NFTs in health care. The use of NFTs in HIE networks could generate a new stream of research for future studies. This study provides practical insights into how the technological foundations of information-sharing efforts in health care have developed and diversified from earlier forms.