In line with the IMO strategy on the reduction in GHG emissions from ships, many alternative fuels are being studied to phase out fossil fuels. Among these new fuel candidates, ammonia has gained significant attention because of its capability to hugely reduce CO₂ emissions. With the introduction of ammonia as a deep-sea vessel fuel, there are growing concerns about ammonia leakage and its influence on crew, ship, and environmental safety. In this study, an innovative formal safety assessment (FSA) framework integrating a hazard and operability study (HAZOP) and Bayesian network was developed to assess the leakage risks of ammonia fuel storage onboard ships. The proposed risk assessment framework was demonstrated by a case study in which refrigerated ammonia was stored in an independent fuel tank underneath the main deck. Three specific risk control options (RCOs) and their combinations were compared based on the cost–benefit analysis. The results indicate that decision-makers may have the option to execute a risk control option from a cost–benefit perspective. This research provides users of onboard ammonia fuel with an approach for assessing storage and usage hazards and estimating and managing their risks.