The recent advancements in machine learning (ML) have demonstrated the potential for providing a powerful solution to build complex prediction systems in a short time. However, in highly regulated industries, such as the financial technology (Fintech), people have raised concerns about the risk of ML systems discriminating against specific protected groups or individuals. To address these concerns, researchers have introduced various mathematical fairness metrics and bias mitigation algorithms. This paper discusses hidden technical debts and challenges of building fair ML systems in a production environment for Fintech. We explore various stages that require attention for fairness in the ML system development and deployment life cycle. To identify hidden technical debts that exist in building fair ML system for Fintech, we focus on key pipeline stages including data preparation, model development, system monitoring and integration in production. Our analysis shows that enforcing fairness for production-ready ML systems in Fintech requires specific engineering commitments at different stages of ML system life cycle. We also propose several initial starting points to mitigate these technical debts for deploying fair ML systems in production.