A nanozyme is a nanoscale material having enzyme-like properties. It exhibits several superior properties, including low preparation cost, robust catalytic activity, and long-term storage at ambient temperatures. Moreover, high stability enables repetitive use in multiple catalytic reactions. Hence, it is considered a potential replacement for natural enzymes. Enormous research interest in nanozymes in the past two decades has made it imperative to look for better enzyme-mimicking materials for biomedical applications. Given this, research on metal-organic frameworks (MOFs) as a potential nanozyme material has gained momentum. MOFs are advanced hybrid materials made of inorganic metal ions and organic ligands. Their distinct composition, adaptable pore size, structural diversity, and ease in the tunability of physicochemical properties enable MOFs to mimic enzyme-like activities and act as promising nanozyme candidates. This review aims to discuss recent advances in the development of MOF-based nanozymes (MOF-NZs) and highlight their applications in the field of biomedicine. Firstly, different enzyme-mimetic activities exhibited by MOFs are discussed, and insights are given into various strategies to achieve them. Modification and functionalization strategies are deliberated to obtain MOF-NZs with enhanced catalytic activity. Subsequently, applications of MOF-NZs in the biosensing and therapeutics domain are discussed. Finally, the review is concluded by giving insights into the challenges encountered with MOF-NZs and possible directions to overcome them in the future. With this review, we aim to encourage consolidated efforts across enzyme engineering, nanotechnology, materials science, and biomedicine disciplines to inspire exciting innovations in this emerging yet promising field.