Acute Pancreatitis (AP) is a medical condition that can eventually lead people to death. Predicting mortality associated with AP allows for more efficient resource allocation, ensuring timely and effective interventions to potentially prevent fatalities. Artificial Intelligence (AI) techniques have been successfully used in this regard. However, ensuring data privacy remains a significant concern when dealing with healthcare data and traditional AI methods may not adequately address this issue. Hence, Federated Learning (FL) rises as an interesting solution to train predictive models securely. In this study, FL was employed to develop a predictor for acute pancreatitis mortality while safeguarding data privacy. The model achieved an accuracy of 0.903, recall of 0.938, and specificity of 0.942 using data from the MIMIC-IV dataset. Comparative analysis with conventional Machine Learning (ML) methods - Logistic Regression, Decision Tree, Random Forest, Multi-layer Percepton and Support Vector Classifier - revealed similar performance, indicating no significant difference in metric values between traditional ML and FL. Moreover, Federated Averaging (FedAvg) performed comparably to the other two FL aggregation algorithms - Federated Adam and Federated Adagrad - although FedAvg performed slightly better in terms of metrics. This reinforces the utilization of FL in healthcare applications, especially considering the significance of data privacy within this domain.