Birth Apshyxia (BA) is a severe condition characterized by insufficient supply of oxygen to a newborn during the delivery. BA is one of the primary causes of neonatal death in the world. Although there has been a decline in neonatal deaths over the past two decades, the developing world, particularly sub-Saharan Africa, continues to experience the highest under-five (<5) mortality rates. While evidence-based methods are commonly used to detect BA in African healthcare settings, they can be subject to physician errors or delays in diagnosis, preventing timely interventions. Centralized Machine Learning (ML) methods demonstrated good performance in early detection of BA but require sensitive health data to leave their premises before training, which does not guarantee privacy and security. Healthcare institutions are therefore reluctant to adopt such solutions in Africa. To address this challenge, we suggest a federated learning (FL)-based software architecture, a distributed learning method that prioritizes privacy and security by design. We have developed a user-friendly and cost-effective mobile application embedding the FL pipeline for early detection of BA. Our Federated SVM model outperformed centralized SVM pipelines and Neural Networks (NN)-based methods in the existing literature